Polynomials

Problem 801

Find the coefficient in $8 x^{2}+1$ . A. 2 B. 8 C. 1 D. $x$

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Problem 802

Which option shows the polynomial $2 x^{2}-4 x+x^{6}+8+3 x^{10}$ in descending order?

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Problem 803

Factor the expression: $6a - 48$

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Problem 804

Factor the following expressions:
1. $45, 70, 85$
2. $35, 49, 77$
3. $x^{5} y^{3}, x^{6} y^{6}$
4. $x^{7} y^{2} z, x^{9} y^{4} z^{2}$
5. $98 x^{5} y^{3}, 110 x^{4} y^{4}, 26 x^{2} y^{5}$
6. $18 x^{7} y^{3} z, 42 x^{3} y^{4} z, 72 x^{4} y z^{2}$
7. $-15 x y z, -55 x y^{2}, -55 y z$
8. $9 x^{3} y^{7}, -18 x y^{2}, -36 y^{3}$
9. $32 x^{5} y^{3}, 48 x^{4} y^{3}, -48 x^{5} y^{4}$
10. $24 x^{4} y^{3}, 84 x^{4} y^{3}, 168 x^{5} q^{4}$
11. $6 a - 48$
12. $21 b + 63 b^{2}$
13. $12 c - 28 d + 52$
14. $-4 e^{2} + 7 e^{3} - 9 e^{4}$
15. $14 f^{3} + 42 f^{5} - 77 f^{7}$
16. $24 g^{2} - 39 g h + 51 h^{2}$
17. $42 j^{2} k - 78 j k^{3} + 66 j^{3} k^{4}$
18. $18 m^{4} n^{4} - 63 m^{5} n^{3} + 117 m^{6} n^{2}$
19. $-8 p^{3} q - 16 p^{2} - p^{8} q$
20. $36 r s^{2} - 72 r^{2} s + 60 r s$

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Problem 805

Find the values of (i) $\frac{1}{\alpha}+\frac{1}{\beta}$ , (ii) $\alpha^{2}+\beta^{2}$ , (iii) $\alpha^{3}+\beta^{3}$ for zeros of $p(x)=3x^{2}-2x-6$ .

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Problem 806

Simplify the expression: $-3(x-7)+4(2x-5)-1$ .

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Problem 807

Simplify: $-4(3x + 2) - (2x + 1) - 3(x + 5)$ .

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Problem 808

Simplify this expression: $-2(8x - 11) + 10x$

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Problem 809

Expand the binomial expression $(x-5)(x+2)$ .

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Problem 810

Encuentra el grado del polinomio $5 x^{3}+3 x^{3}-2 x^{2}+x-3$ .

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Problem 811

Factor $81 a^{2} b$ and choose the correct option: A) $2 \cdot 3 \cdot 13 \cdot a^{2} \cdot b$ , B) $2 \cdot 3 \cdot 13 \cdot a^{2} \cdot b^{2}$ , C) $3^{4} \cdot a^{2} \cdot b$ , D) $2 \cdot 41 \cdot a^{2} \cdot b$ .

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Problem 812

Simplify the expression $\left[\left(-3 a^{2}\right)^{2}-(-2 a)\left(-3 a^{3}\right)\right]^{3}$ .

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Problem 813

Simplify the expression $\left[\left(-2 x^{3}\right)^{2}-(-2 x)^{2}\left(+3 x^{4}\right)\right]:\left(-2 x^{3}\right)$ .

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Problem 814

Find the min and max of $\tau=x^{2}+y^{3}-3 x+2124$ given $x=0$ , $y=0$ , and $x+y=3$ .

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Problem 815

Simplify the expression: $(-2 u^{3} v) : (-4 u v) + (-4 u^{5} v^{6}) : (2 u^{5} v^{4}) + 2.5 u^{2}$ .

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Problem 816

Simplify the expression: $\left[\left(-\frac{1}{2} a^{3} b\right)^{3}:\left(\frac{1}{4} a^{6} b^{2}\right)+\left(-2 a b\right)^{3}:\left(-2 b^{2}\right)\right]\left[(-3 a b)(-2 b^{3})-(-2 a b)(-2 b^{2})\right]$

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Problem 817

Simplify the expression: $(-2 a)^{2}-3 a(-2 a)+4 b(-b)^{2}+(-2 b)^{3}+\left(-2 a b^{5}\right):\left(-2 b^{2}\right)$ .

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Problem 818

Simplify the expression: $-2 x(2 x)+\left(-9 x^{2} y^{3}\right):\left(3 x^{2} y\right)+(-34)^{2}-x^{2}-(-2 y)(-34)$ .

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Problem 819

Find the equivalent expression for $(2 x+3)^{2}+(2 x+3)(x-1)-2(4 x^{2}-9)$ .

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Problem 820

Evaluate the function $b(t)=4 t^{3}-t^{2}$ at $t=-2$ . What is $b(-2)$ ?

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Problem 821

Evaluate the function $f(x) = x^{3} - 6x$ at $x = -3$ . What is $f(-3)$ ?

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Problem 822

Simplify the expression: $8 k^{2} - k - 5 k + 7 - 2 k^{2}$ .

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Problem 823

Combine like terms in the expression: $-4 a^{2} b + 7 + 10 a^{2} b$ .

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Problem 824

Siven the function below, determine the following. $f(x)=4 x^{3}-5 x$
Find $f(-x)$ . $f(-x)=$
Select all true statements below. $f(-x)=f(x)$ $f(-x)=-f(x)$ $f$ is an odd function $f$ is an even function $f$ is neither an odd nor even function

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Problem 825

Find each product. Simplify completely. a) $(x+3)(x-3)$ b) $(x+\sqrt{3})(x-\sqrt{3})$ c) $(a-b)(a+b)$

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Problem 826

Holden Warren Question 16 of 24
Find each product. Simplify completely. a) $(x-5)\left(x^{2}+5 x+25\right)$ b) $(x+3)\left(x^{2}-3 x+9\right)$

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Problem 827

Holden Warren Question 24 of 24 PREV NEXT
Find the product. Collect all like terms. $(4 p-7 q)(4 p+7 q)$ \begin{tabular}{lc} \hline Question 1 & $100 \%$ \\ \hline Question 2 & $100 \%$ \\ Question 3 & $100 \%$ \\ Question 4 & $100 \%$ \\ \hline Question 5 & $100 \%$ \\ Question 6 & $100 \%$ \\ Question 7 & $100 \%$ \end{tabular}

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Problem 828

(a) Complete this synthetic division table. $\begin{array}{lllll} \\ -5) & 1 & 6 & 4 & -5\end{array}$ $\square \quad \square$ $\square \square \square$ (b) Write your answer in the following form: Quotient $+\frac{\text { Remainder }}{x+5}$ . $\frac{x^{3}+6 x^{2}+4 x-5}{x+5}=\square+\frac{\square}{x+5}$

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Problem 829

a) $\left(3 x^{2}-4 x-11\right)-\left(2 x^{2}+3 x-2\right)$ b) $(4 x-7)(5 x+1)$ $c\left(x^{2}-1\right)(2 x+3)$

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Problem 830

Factor. (There is more than one step in factoring these problems. Be sure they are factored completely.)
18. $4 s^{2}+16 s-128=$
19. $5 x^{2}-5 x-150=$
20. $a^{3}-a b^{2}=$
21. $2 t^{2} x+28 t x+96 x=$
22. $x^{4}-y^{4}=$
23. $2 a x^{2}-4 a x-6 a=$
24. $4 x^{2}-16 x+16=$
25. $3 a^{2} b-6 a b-72 b=$

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Problem 831

Find all zeros 1) $f(x)=x^{6}+8 x^{5}-114 x^{4}-428 x^{3}+3149 x^{2}+4356 x-16380$
HINT: $2,5,7$ and -6 are zeros 2) $g(x)=2 x^{4}-21 x^{3}+155 x^{2}-44 x-222$
HINT: $3 / 2$ and -1 are zeros 3) $h(x)=x^{5}+7 x^{4}+10 x^{3}-27 x^{2}-189 x-270$
HINT:-5 and -2 are zeros 4) $k(x)=x^{5}-5 x^{4}-3 x^{3}+15 x^{2}-28 x+140$
HINT: 5 is a zero

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Problem 832

Simplify the expression. $20-10 b-21+b-3$

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Problem 833

The $y$ -intercept of the function $y=0.5 x^{3}-2.5 x^{2}+0.1 x+10$ is Select one: a. -2.5 b. 0.5 c. 10 d. 0.1

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Problem 834

estions $1-3$ , consider the expression $18 w^{4} m^{2}-27 w^{5} m$ Vhat is the greatest common factor (GCF) of the two terms in the

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Problem 835

Factor the following. Be sure to factor each one completely.
18. $2 a^{2} x+16 a b x+32 b^{2} x=$
19. $100 x^{2}-64=$
20. $y^{4}-16=$
21. $4 x^{2}-9 y^{2}=$
22. $x^{2}-6 x+9=$
23. $4 a^{2} b^{2}-12 a b+9=$

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Problem 836

Simplify the expression:
$\frac{y^{2}}{2} - \frac{7y}{2}$

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Problem 837

Using the rational root theorem, list out all possible/candidate rational roots of $f(x)=-6 x^{4}+23 x^{3}-4 x^{2}-12 x+9$ . Express your answer as integers or as fractions in simplest form. Use commas to separate.

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Problem 838

Find the real zeros of $f$ and state the multiplicity for each zero. State whether the graph of $f$ crosses or touches the $x$ -axis at each zero. $f(x)=\left(x^{2}+6\right)(4 x-3)^{2}$
Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or simplified fractions.) A. The real zero of $f$ is $\square$ with multiplicity $\square$ and the graph of f crosses the x -axis at this zero. B. The real zero of $f$ is $\square$ with multiplicity $\square$ and the graph of $f$ touches but does not cross the $x$ -axis at this zero. C. The smallest real zero of $f$ is $\square$ with multiplicity $\square$ and the graph of $f$ touches but does not cross the $x$ -axis at this zero. The largest real zero of $f$ is $\square$ with multiplicity $\square$ and the graph of $f$ touches but does not cross the $x$ -axis at this zero. D. The smallest real zero of $f$ is $\square$ with multiplicity $\square$ and the graph of $f$ crosses the $x$ -axis at this zero. The largest real zero of $f$ is $\square$ with multiplicity $\square$ and the graph of $f$ touches but does not cross the $x$ -axis at this zero.

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Problem 839

Wibek of: Secion b. I-wriam venuns
14. For the polynomial function $f(x)=-2 x^{2}\left(x^{2}-5\right)$ inswer the following questions. (a) List each real zero and its mulliplicily. (b) Determine whether the graph crosses or louches the $x$ -axis at each $x$ -intercepl. (c) Delermine the maximum number of turning poinis on the graph. (d) Determine the end behavior; that is, find the power function that tho graph of fresembles for farge values of |al. (a) Find any real zeros of t . Select the correct choice below and, if necessang, fill in the answer bax(es) to complate your choice. O. The real zero of $f$ is with multiplicily (Type an exact answer, using radicals as needed. Type iniegers or fractions.) B. The smallest zero of II with muliplicity $\qquad$ The largesizero of tis $\qquad$ with multiplicity (Type an exaci ansiver, using radicals as needed. Type inlegers or fraclions.) C. The smallest zero of I is with multiplicily
The midale zero of its $\qquad$ muliplicily .The largesi zero of tis with muliplicity with (Type an exach answer, using radicals as needed. Type inlegers or fraclions.) D. There are no real zeros. (b) Select the correct cholce below and, it necessary, fill in the answer box(es) to complete your choice. A. The graph fouches the x-axis at (Type an exact answer, using radicals as needed. Type an inleger or a simplified fraction. Use a comma to separale answers as needed.) B. The graph crosses the $x$ -axis at (Type an exacl answer, using radicals as needed. Type an inleger or a simplified fraction. Use a comma to separate answers as needed.) C. The graph louches the $x$ -axis at and crosses at (Type integers or simplified fractions. Use a comma lo separale answers as needed.) D. The graph neither crosses nor fouches the $x$ -axis. (c) The maximum number of furning points on the graph is $\square$ (Type a whole number.) (d) The power function that the graph of f resembles for large values of $|x|$ is $y=\mid$ $\square$

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Problem 840

Factor $18 v^{9}+33 v^{8}+14 v^{7}$ completely.

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Problem 841

Determine whether each expression is a monomial. Write yes or no. Explain your reasoning.
22. $3 a^{4}$
24. $\frac{-2 g}{4 h}$ $26.6 m+3 n$

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Problem 842

$-21 r^{7} p^{5} + 15 r^{3} p$

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Problem 843

Find the polynomial with a leading coefficient of either 1 or -1 and with smallest possible degree that matches the given graph.
The polynomial function is $f(x)=$ $\square$

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Problem 844

4. Sisa pembagian suku banyak $P(x)$ terhadap $\left(x^{2}-1\right)$ adalah $(12 x-23)$ . Sisa pembagian suku banyak $P(x)$ terhadap $(x-2)$ adalah 1 . Sisa pembagian suku banyak $P(x)$ terhadap tehadap $\left(x^{2}-3 x+2\right)$ adalah.. A. $12 x-23$ B. $-12 x+1$ C. $-10 x+1$ D. $24 x+1$ E. $24 x-27$

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Problem 845

Use a combination of factoring methods to factor the polynomial. $(4 p+q) r^{2}-9(4 p+q) r+20(4 p+q)$
Select the correct choice below and fill in any answer boxes within your choice. A. $(4 p+q) r^{2}-9(4 p+q) r+20(4 p+q)=$ $\square$ B. The polynomial is prime.

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Problem 846

\begin{tabular}{|l|c|} \hline \multirow{2}{*}{ Function } & Is the function a polynomial? \\ \cline { 2 - 3 } (a) $u(x)=6 x^{-3}+4 x$ & Yes \\ (b) $v(x)=4(x-4)(x+2)$ & No \\ (c) $g(x)=2-\frac{4}{x}$ & \\ (d) $f(x)=-8 \sqrt{x}$ & \\ \hline \end{tabular}

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Problem 847

For the polynomial below, 3 is a zero. $f(x)=x^{3}-2 x^{2}-5 x+6$
Express $f(x)$ as a product of linear factors. $f(x)=$

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Problem 848

For the polynomial below, 1 is a zero. $h(x)=x^{3}+3 x^{2}-2 x-2$
Express $h(x)$ as a product of linear factors. $h(x)=$

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Problem 849

Using the remainder theorem to
Use the remainder theorem to find $P(1)$ for $P(x)=-x^{4}+3 x^{3}+4 x^{2}-4$ . Specifically, give the quotient and the remainder for the associated division and the value of $P(1)$ . $\square$

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Problem 850

Use synthetic division to simplify $\frac{x^{3}-6 x-9}{x-3}$

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Problem 851

Use synthetic division to find $\left(x^{2}-20\right) \div(x-1)$

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Problem 852

Determine the total number of solutions to each polynomial equation. a) The polynomial equation $-2 x^{4}+x+3=0$ has exactly $\square$ solutions. b) The polynomial equation $3 x^{5}+8 x^{4}+7 x^{3}=0$ has exactly $\square$ solutions. c) The polynomial equation $-x^{2}+x+6=0$ has exactly $\square$ solutions. Question Help: Video Written Example

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Problem 853

Find all the real zeros of $f(x)=x^{4}-5 x^{3}-11 x^{2}+79 x-84$ . Enter the zeros separated by commas. Enter exact values, not decimal approximations. $\square$ Submit Question

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Problem 854

Polynomials 7 Enter an expression that is equivalent to the expression below in the form $x^{m} y^{n}$ $\left(x^{5} y^{2} y^{1}\right)^{5}$

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Problem 855

Instrucción IX: Calcula el resultado de las siguientes expresiones utilizando áreas geométricas. a) $(x+3)(x+5)=$ b) $(x+4)(x+6)=$ c) $(x+2)(x+4)=$

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Problem 856

9.1 For each polynomial given below, find the degree, the leading term, the leading coemcient, and the constant term. (a) $f(x)=-\frac{1}{2} x+3 x^{4}$ (b) $g(x)=\left(\frac{1}{3} x^{2}-3\right)(5+2 x)^{2}$ (c) $f(x)+g(x)$ (d) $f(x) \cdot g(x)$ 9.2 (a) Set up the sign diagrams and determine the end behaviour for the polynomials from exercise 9.1 .

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Problem 857

Given $f(x)=(x+8)(x+7)(x+2)$ find the roots give your answers $x_{1} \leq x_{2} \leq x_{3}$ $\begin{array}{l} x_{1}=\square \\ x_{2}=\square \\ x_{3}=\square \end{array}$
Find the $y$ -intercept $=(0$ , $\square$

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Problem 858

Add the polynomials. $\left(\frac{1}{2} x^{3}+3 x^{2}+\frac{27}{4}\right)+\left(\frac{9}{7} x^{3}-\frac{4}{5} x^{2}-5 x\right)$

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Problem 859

Example 5 Solve a Polynomial by Grouping Solve a polynomial by grouping: $x^{3}+x^{2}-9 x-9=0$ .

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Problem 860

Factor the polynomial completely, if possible. If the expression cannot be factored, enter the expression as is. $704 q^{3}-539 q$

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Problem 861

Factor the following expression. $27 x^{3} y^{18}-512$ A. $\left(3 x y^{6}-8\right)\left(9 x^{2} y^{12}+24 x y^{6}+64\right)$ B. $\left(3 x y^{6}-8\right)\left(9 x^{2} y^{12}-24 x y^{6}+64\right)$ C. $\left(3 x y^{6}+8\right)\left(9 x^{2} y^{12}-24 x y^{6}-64\right)$ D. $\left(3 x y^{6}+8\right)\left(9 x^{2} y^{12}+24 x y^{6}-64\right)$

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Problem 862

What are the zeros and their multiplicities for the function $y=x^{3}+3 x^{2}+x+3$ , shown in the graph?

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Problem 863

When factored completely, $m^{5}+m^{3}-6 m$ is equivalen 1) $(m+3)(m-2)$ 2) $\left(m^{2}+3 m\right)\left(m^{2}-2\right)$ 3) $m\left(m^{4}+m^{2}-6\right)$ 4) $m\left(m^{2}+3\right)\left(m^{2}-2\right)$

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Problem 864

Question 21
Consider the polynomial $19 x^{6}+21 x^{4}-11 x^{3}-12 x+12$ . What is the degree of the polynomial? $\qquad$ Identify the constant term. $\qquad$ What is the coefficient of the first term? $\qquad$

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Problem 865

Solve $x^{4}-24 x^{3}+216 x^{2}-864 x+1296=0$ . State the solution rounded to one decimal place.

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Problem 866

3. $(18-a b)+4 b \quad$ (if $a=-2$ and $b=-5$ )

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Problem 867

Question Watch Video Show Examples Use synthetic division to find the result when $4 x^{4}+11 x^{3}+17 x^{2}+x-9$ is divided by $x+1$ .

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Problem 868

Error Analysis A gardener plans to extend the length of a rectangular garden by 2 feet Let $\times$ represent the garden's original length. The expression $9(x+2)$ represents the area of the garden, where 9 the width, in feet, and ( $x+2$ ) represents the extended length, In feet, of the garden. When asked for the area of the extended portion, the gardener incorrectly said it was 11 square feel Expand the expression to find the area of the extension. Then describe an error the gardener might have made
Which answer below represents the correct expansion and the correct area of the extension? A. $9 x+18$ ; the area of the extension is $9 x$ square feet. B. $9 x+2$ , the area of the extension is 2 square feet. C. $9 x+18$ , the area of the extension is 18 square feet. D. $10 x+11$ , the area of the extension is $10 x$ square feet. Cloar all

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Problem 869

An archited plans to build an extension to Meiling's rectangular deck Let $x$ represent the increase, in meters, of her deck's length The expression $3(x+9)$ represents the area of the deck, where 3 is the width, in meters, and ( $x+9$ ) represents the extended length, in meters. Use the Distributive Property to write an expression that represents the total area of Mliling's new deck
Click the icon to view the deck
An expression that represents the total area of Meiling's new deck is $\square$ (Simplify your answer. Use integers or decimals for any numbers in the expression.) Help me solve this View an example Get more help - Clear all Check answer Roviow Progross Question 11 of 13 Back Noxt Search 1139 AM 11/21/2024

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Problem 870

Question 11 1 pts
The function $f(x)=\frac{2}{5} x^{5}-2 x^{4}-\frac{2}{3} x^{3}+16 x^{2}-24 x-3$ has 4 critical numbers. Three of the critical numbers are $x=2, x=-2$ and $x=3$ . What is the 4 th critical number? Do not include $x=$ in your answer. Just type the critical number. e.g. 7 $\square$

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Problem 871

Exercice 6: Montrer que: $(\forall x \in \mathbb{R}): \quad x^{6}-x^{5}+x^{4}-x^{3}+x^{2}-x+\frac{3}{4} \leq 0$ Indication Discuter les cas $x \geq 1, x \leq 0$ et $0<x<1$ .

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Problem 872

1 (a) Expand $7(2 x+7)$ (b) Factorise $3 y+12$
2 (a) Expand $5 a(a-6)$ (b) Solve $4(b+2)=24$
3 (a) Factorise fully $12 m+8 m^{2}$ (b) Solve $3(n-5)=27$

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Problem 873

$\frac{15 x^{7}-11 x^{6}+25 x^{5}-20 x^{4}}{-5 x^{4}}=$ (Simplify your answer.)

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Problem 874

Factor the following expression by grouping. $5 x^{2}-15 x y+2 x y-6 y^{2}$

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Problem 875

Find all the zero(s) of the function $P(x)=x^{3}-3 x^{2}+x-3$
A $\{-1,-3\}$
B $\{3,-1,1\}$
C $\{1,3 i,-3 i\}$
D $\{3,-i, i\}$ $E^{-}\{-1,1,-3 i\}$
F None of the above

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Problem 876

Factor the following function: $x^{4}+3 x^{3}-15 x^{2}-19 x+30$ . How many real-valued roots does this polynomial have?

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Problem 877

Question Watch Video Show Examples
Use synthetic division to find the result when $4 x^{4}+17 x^{3}+9 x^{2}-16 x+4$ is divided by $x+2$ .

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Problem 878

Find $(f \circ g)(x)$ . $\begin{array}{l} f(x)=-2 x+10 \\ g(x)=-x-3 \end{array}$
Write your answer as a polynomial in simplest form. $(f \circ g)(x)=$ $\square$

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Problem 879

Factorise fully the following: a) $x^{2}+3 x$ b) $2 x^{2}-8 x$ c) $6 x+9 x^{3}$ d) $12 x^{3}-4 x^{2}$

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Problem 880

What is $(q-s)(x)$ ? $\begin{array}{l} q(x)=3 x^{2}-x-4 \\ s(x)=2 x \end{array}$
Write your answer as a polynomial or a rational function in simplest form.

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Problem 881

(x) What is $(f+g)(x)$ ? $\begin{array}{l} f(x)=2 x^{2}+10 x \\ g(x)=-5 x+1 \end{array}$ [ax.] Write your answer as a polynomial or a rational function in simplest form.

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Problem 882

What is $(f+g)(x)$ ? $\begin{array}{l} f(x)=-5 x \\ g(x)=x^{2}-4 x-5 \end{array}$ ) 路A, Write your answer as a polynomial or a rational function in simplest form.

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Problem 883

Factor the trinomial completely. If the trinomial contains a greatest common factor (other than 1 ), factor out the GCF first. $175-60 m+5 m^{2}$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $175-60 m+5 m^{2}=$ $\square$ (Factor completely.) B. The polynomial is prime.

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Problem 884

Factor the following trinomial. Remember to factor out the greatest common factor as the first step. $9 q^{2}(m+1)^{2}-3 q(m+1)^{2}-2(m+1)^{2}$
Select the correct choice below and fill in any answer boxes within your choice. A. $9 q^{2}(m+1)^{2}-3 q(m+1)^{2}-2(m+1)^{2}=$ $\square$ B. The polynomial is prime.

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Problem 885

Factor each expression.
27. $27+12=$ $3(13)$
30. $2 x+8=$

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Problem 886

Write the following in factored form by factoring out the greatest common factor. $r(y-3)+s(y-3)$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $r(y-3)+s(y-3)=$ $\square$ B. There is no common factor other than 1.

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Problem 887

the coordinate plane and label the zeros. diction. $8 g(x)=(x-5)(x+5)(x-5)$

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Problem 888

Find the sum of the constants $a$ , $b$ , and $c$ in the polynomial $G(x)=(x-a)(x-b)(x-c)$ with zeros $5, -\frac{3}{2}, \frac{1}{2}$ .

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Problem 889

Expand the expression $(a-2 b)^{2}$ .

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Problem 890

简化： $-6 h^{2}+2 j-14 h^{2}-h^{2}+15 j$ 选择答案： $-20 h^{2}+13 j$ ， $20 h^{2}+17 j$ ， $-21 h^{2}+17 j$ ， $-21 h^{4}+17 j$ 。

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Problem 891

Simplify the expression: $(4 x^{3}-5 x^{2}+3 x) + (-2 x^{3}-x^{2}+6 x)$ . What is the result?

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Problem 892

Expand the expression $(4 x-5)(x+3)$ .

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Problem 893

Simplify $(3 x-1)(x+2)$ using the distributive property or FOIL method.

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Problem 894

Tính tích các đơn thức sau và xác định hệ số, bậc của từng đa thức: a) $A=-2 x^{4} ; B=\frac{3}{4} x^{6}$ b) $A=\frac{1}{5} x^{3} ; B=\left(-\frac{4}{3} x\right)^{2} ; C=2 x$ .

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Problem 895

Calculate the expression when $a=-2$ : $9+a^{2}+a^{3}+a^{4}$ .

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Problem 896

Simplify $(1+4 x)(3 x^{2}-2 x)+(x-3)$ .

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Problem 897

Simplify $\frac{a^{4}-c^{4}}{(a+c)^{2}(a^{2}+c^{2})}$ .

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Problem 898

Expand and simplify $(3-x)(x-4)$ .

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Problem 899

Solve for $x$ in the equation $x(x^{3}+x^{3})-2x \div x - 1 = -(x+1)(x+3) + (x^{2}+x^{2})^{2}$ . Which expression equals zero?

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Problem 900

Solve the equation: $(4 p-1)(5 p+3)=20(p-1)^{2}-258$ . Find $p=$

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1 ...6 7 8 9 10 11 12 ...25

Polynomials

Problem 801

Find the coefficient in 8x2+18 x^{2}+18x2+1. A. 2 B. 8 C. 1 D. xxx

Problem 802

Which option shows the polynomial 2x2−4x+x6+8+3x102 x^{2}-4 x+x^{6}+8+3 x^{10}2x2−4x+x6+8+3x10 in descending order?

Problem 803

Factor the expression: 6a−486a - 486a−48

Problem 804

Problem 805

Find the values of (i) 1α+1β\frac{1}{\alpha}+\frac{1}{\beta}α1​+β1​, (ii) α2+β2\alpha^{2}+\beta^{2}α2+β2, (iii) α3+β3\alpha^{3}+\beta^{3}α3+β3 for zeros of p(x)=3x2−2x−6p(x)=3x^{2}-2x-6p(x)=3x2−2x−6.

Problem 806

Simplify the expression: −3(x−7)+4(2x−5)−1-3(x-7)+4(2x-5)-1−3(x−7)+4(2x−5)−1.

Problem 807

Simplify: −4(3x+2)−(2x+1)−3(x+5)-4(3x + 2) - (2x + 1) - 3(x + 5)−4(3x+2)−(2x+1)−3(x+5).

Problem 808

Simplify this expression: −2(8x−11)+10x-2(8x - 11) + 10x−2(8x−11)+10x

Problem 809

Expand the binomial expression (x−5)(x+2)(x-5)(x+2)(x−5)(x+2).

Problem 810

Encuentra el grado del polinomio 5x3+3x3−2x2+x−35 x^{3}+3 x^{3}-2 x^{2}+x-35x3+3x3−2x2+x−3.

Problem 811

Problem 812

Simplify the expression [(−3a2)2−(−2a)(−3a3)]3\left[\left(-3 a^{2}\right)^{2}-(-2 a)\left(-3 a^{3}\right)\right]^{3}[(−3a2)2−(−2a)(−3a3)]3.

Problem 813

Simplify the expression [(−2x3)2−(−2x)2(+3x4)]:(−2x3)\left[\left(-2 x^{3}\right)^{2}-(-2 x)^{2}\left(+3 x^{4}\right)\right]:\left(-2 x^{3}\right)[(−2x3)2−(−2x)2(+3x4)]:(−2x3).

Problem 814

Find the min and max of τ=x2+y3−3x+2124\tau=x^{2}+y^{3}-3 x+2124τ=x2+y3−3x+2124 given x=0x=0x=0, y=0y=0y=0, and x+y=3x+y=3x+y=3.

Problem 815

Simplify the expression: (−2u3v):(−4uv)+(−4u5v6):(2u5v4)+2.5u2(-2 u^{3} v) : (-4 u v) + (-4 u^{5} v^{6}) : (2 u^{5} v^{4}) + 2.5 u^{2}(−2u3v):(−4uv)+(−4u5v6):(2u5v4)+2.5u2.

Problem 816

Problem 817

Simplify the expression: (−2a)2−3a(−2a)+4b(−b)2+(−2b)3+(−2ab5):(−2b2)(-2 a)^{2}-3 a(-2 a)+4 b(-b)^{2}+(-2 b)^{3}+\left(-2 a b^{5}\right):\left(-2 b^{2}\right)(−2a)2−3a(−2a)+4b(−b)2+(−2b)3+(−2ab5):(−2b2).

Problem 818

Simplify the expression: −2x(2x)+(−9x2y3):(3x2y)+(−34)2−x2−(−2y)(−34)-2 x(2 x)+\left(-9 x^{2} y^{3}\right):\left(3 x^{2} y\right)+(-34)^{2}-x^{2}-(-2 y)(-34)−2x(2x)+(−9x2y3):(3x2y)+(−34)2−x2−(−2y)(−34).

Problem 819

Find the equivalent expression for (2x+3)2+(2x+3)(x−1)−2(4x2−9)(2 x+3)^{2}+(2 x+3)(x-1)-2(4 x^{2}-9)(2x+3)2+(2x+3)(x−1)−2(4x2−9).

Problem 820

Evaluate the function b(t)=4t3−t2b(t)=4 t^{3}-t^{2}b(t)=4t3−t2 at t=−2t=-2t=−2. What is b(−2)b(-2)b(−2)?

Problem 821

Evaluate the function f(x)=x3−6xf(x) = x^{3} - 6xf(x)=x3−6x at x=−3x = -3x=−3. What is f(−3)f(-3)f(−3)?

Problem 822

Simplify the expression: 8k2−k−5k+7−2k28 k^{2} - k - 5 k + 7 - 2 k^{2}8k2−k−5k+7−2k2.

Problem 823

Combine like terms in the expression: −4a2b+7+10a2b-4 a^{2} b + 7 + 10 a^{2} b−4a2b+7+10a2b.

Problem 824

Problem 825

Find each product. Simplify completely. a) (x+3)(x−3)(x+3)(x-3)(x+3)(x−3) b) (x+3)(x−3)(x+\sqrt{3})(x-\sqrt{3})(x+3​)(x−3​) c) (a−b)(a+b)(a-b)(a+b)(a−b)(a+b)

Problem 826

Holden Warren Question 16 of 24Find each product. Simplify completely. a) (x−5)(x2+5x+25)(x-5)\left(x^{2}+5 x+25\right)(x−5)(x2+5x+25) b) (x+3)(x2−3x+9)(x+3)\left(x^{2}-3 x+9\right)(x+3)(x2−3x+9)

Problem 827

Problem 828

Problem 829

a) (3x2−4x−11)−(2x2+3x−2)\left(3 x^{2}-4 x-11\right)-\left(2 x^{2}+3 x-2\right)(3x2−4x−11)−(2x2+3x−2) b) (4x−7)(5x+1)(4 x-7)(5 x+1)(4x−7)(5x+1) c(x2−1)(2x+3)c\left(x^{2}-1\right)(2 x+3)c(x2−1)(2x+3)

Problem 830

Problem 831

Problem 832

Simplify the expression. 20−10b−21+b−320-10 b-21+b-320−10b−21+b−3

Problem 833

The yyy-intercept of the function y=0.5x3−2.5x2+0.1x+10y=0.5 x^{3}-2.5 x^{2}+0.1 x+10y=0.5x3−2.5x2+0.1x+10 is Select one: a. -2.5 b. 0.5 c. 10 d. 0.1

Problem 834

estions 1−31-31−3, consider the expression 18w4m2−27w5m18 w^{4} m^{2}-27 w^{5} m18w4m2−27w5m Vhat is the greatest common factor (GCF) of the two terms in the

Problem 835

Problem 836

Simplify the expression: y22−7y2\frac{y^{2}}{2} - \frac{7y}{2}2y2​−27y​

Problem 837

Using the rational root theorem, list out all possible/candidate rational roots of f(x)=−6x4+23x3−4x2−12x+9f(x)=-6 x^{4}+23 x^{3}-4 x^{2}-12 x+9f(x)=−6x4+23x3−4x2−12x+9. Express your answer as integers or as fractions in simplest form. Use commas to separate.

Problem 838

Problem 839

Problem 840

Factor 18v9+33v8+14v718 v^{9}+33 v^{8}+14 v^{7}18v9+33v8+14v7 completely.

Problem 841

Determine whether each expression is a monomial. Write yes or no. Explain your reasoning.22. 3a43 a^{4}3a424. −2g4h\frac{-2 g}{4 h}4h−2g​ 26.6m+3n26.6 m+3 n26.6m+3n

Problem 842

−21r7p5+15r3p-21 r^{7} p^{5} + 15 r^{3} p−21r7p5+15r3p

Problem 843

Find the polynomial with a leading coefficient of either 1 or -1 and with smallest possible degree that matches the given graph.The polynomial function is f(x)=f(x)=f(x)= □\square□

Problem 844

Problem 845

Problem 846

Problem 847

Find the coefficient in $8 x^{2}+1$ . A. 2 B. 8 C. 1 D. $x$

Which option shows the polynomial $2 x^{2}-4 x+x^{6}+8+3 x^{10}$ in descending order?

Factor the expression: $6a - 48$

Find the values of (i) $\frac{1}{\alpha}+\frac{1}{\beta}$ , (ii) $\alpha^{2}+\beta^{2}$ , (iii) $\alpha^{3}+\beta^{3}$ for zeros of $p(x)=3x^{2}-2x-6$ .

Simplify the expression: $-3(x-7)+4(2x-5)-1$ .

Simplify: $-4(3x + 2) - (2x + 1) - 3(x + 5)$ .

Simplify this expression: $-2(8x - 11) + 10x$

Expand the binomial expression $(x-5)(x+2)$ .

Encuentra el grado del polinomio $5 x^{3}+3 x^{3}-2 x^{2}+x-3$ .

Simplify the expression $\left[\left(-3 a^{2}\right)^{2}-(-2 a)\left(-3 a^{3}\right)\right]^{3}$ .

Simplify the expression $\left[\left(-2 x^{3}\right)^{2}-(-2 x)^{2}\left(+3 x^{4}\right)\right]:\left(-2 x^{3}\right)$ .

Find the min and max of $\tau=x^{2}+y^{3}-3 x+2124$ given $x=0$ , $y=0$ , and $x+y=3$ .

Simplify the expression: $(-2 u^{3} v) : (-4 u v) + (-4 u^{5} v^{6}) : (2 u^{5} v^{4}) + 2.5 u^{2}$ .

Simplify the expression: $(-2 a)^{2}-3 a(-2 a)+4 b(-b)^{2}+(-2 b)^{3}+\left(-2 a b^{5}\right):\left(-2 b^{2}\right)$ .

Simplify the expression: $-2 x(2 x)+\left(-9 x^{2} y^{3}\right):\left(3 x^{2} y\right)+(-34)^{2}-x^{2}-(-2 y)(-34)$ .

Find the equivalent expression for $(2 x+3)^{2}+(2 x+3)(x-1)-2(4 x^{2}-9)$ .

Evaluate the function $b(t)=4 t^{3}-t^{2}$ at $t=-2$ . What is $b(-2)$ ?

Evaluate the function $f(x) = x^{3} - 6x$ at $x = -3$ . What is $f(-3)$ ?

Simplify the expression: $8 k^{2} - k - 5 k + 7 - 2 k^{2}$ .

Combine like terms in the expression: $-4 a^{2} b + 7 + 10 a^{2} b$ .

Find each product. Simplify completely. a) $(x+3)(x-3)$ b) $(x+\sqrt{3})(x-\sqrt{3})$ c) $(a-b)(a+b)$

Holden Warren Question 16 of 24
Find each product. Simplify completely. a) $(x-5)\left(x^{2}+5 x+25\right)$ b) $(x+3)\left(x^{2}-3 x+9\right)$

a) $\left(3 x^{2}-4 x-11\right)-\left(2 x^{2}+3 x-2\right)$ b) $(4 x-7)(5 x+1)$ $c\left(x^{2}-1\right)(2 x+3)$

Simplify the expression. $20-10 b-21+b-3$

The $y$ -intercept of the function $y=0.5 x^{3}-2.5 x^{2}+0.1 x+10$ is Select one: a. -2.5 b. 0.5 c. 10 d. 0.1

estions $1-3$ , consider the expression $18 w^{4} m^{2}-27 w^{5} m$ Vhat is the greatest common factor (GCF) of the two terms in the

Simplify the expression:
$\frac{y^{2}}{2} - \frac{7y}{2}$

Using the rational root theorem, list out all possible/candidate rational roots of $f(x)=-6 x^{4}+23 x^{3}-4 x^{2}-12 x+9$ . Express your answer as integers or as fractions in simplest form. Use commas to separate.

Factor $18 v^{9}+33 v^{8}+14 v^{7}$ completely.

Determine whether each expression is a monomial. Write yes or no. Explain your reasoning.
22. $3 a^{4}$
24. $\frac{-2 g}{4 h}$ $26.6 m+3 n$

$-21 r^{7} p^{5} + 15 r^{3} p$

Find the polynomial with a leading coefficient of either 1 or -1 and with smallest possible degree that matches the given graph.
The polynomial function is $f(x)=$ $\square$

For the polynomial below, 3 is a zero. $f(x)=x^{3}-2 x^{2}-5 x+6$
Express $f(x)$ as a product of linear factors. $f(x)=$

For the polynomial below, 1 is a zero. $h(x)=x^{3}+3 x^{2}-2 x-2$
Express $h(x)$ as a product of linear factors. $h(x)=$

Using the remainder theorem to
Use the remainder theorem to find $P(1)$ for $P(x)=-x^{4}+3 x^{3}+4 x^{2}-4$ . Specifically, give the quotient and the remainder for the associated division and the value of $P(1)$ . $\square$

Use synthetic division to simplify $\frac{x^{3}-6 x-9}{x-3}$

Use synthetic division to find $\left(x^{2}-20\right) \div(x-1)$

Find all the real zeros of $f(x)=x^{4}-5 x^{3}-11 x^{2}+79 x-84$ . Enter the zeros separated by commas. Enter exact values, not decimal approximations. $\square$ Submit Question

Polynomials 7 Enter an expression that is equivalent to the expression below in the form $x^{m} y^{n}$ $\left(x^{5} y^{2} y^{1}\right)^{5}$

Instrucción IX: Calcula el resultado de las siguientes expresiones utilizando áreas geométricas. a) $(x+3)(x+5)=$ b) $(x+4)(x+6)=$ c) $(x+2)(x+4)=$

Add the polynomials. $\left(\frac{1}{2} x^{3}+3 x^{2}+\frac{27}{4}\right)+\left(\frac{9}{7} x^{3}-\frac{4}{5} x^{2}-5 x\right)$

Example 5 Solve a Polynomial by Grouping Solve a polynomial by grouping: $x^{3}+x^{2}-9 x-9=0$ .

Factor the polynomial completely, if possible. If the expression cannot be factored, enter the expression as is. $704 q^{3}-539 q$

What are the zeros and their multiplicities for the function $y=x^{3}+3 x^{2}+x+3$ , shown in the graph?

Question 21
Consider the polynomial $19 x^{6}+21 x^{4}-11 x^{3}-12 x+12$ . What is the degree of the polynomial? $\qquad$ Identify the constant term. $\qquad$ What is the coefficient of the first term? $\qquad$

Solve $x^{4}-24 x^{3}+216 x^{2}-864 x+1296=0$ . State the solution rounded to one decimal place.

3. $(18-a b)+4 b \quad$ (if $a=-2$ and $b=-5$ )

Question Watch Video Show Examples Use synthetic division to find the result when $4 x^{4}+11 x^{3}+17 x^{2}+x-9$ is divided by $x+1$ .

Exercice 6: Montrer que: $(\forall x \in \mathbb{R}): \quad x^{6}-x^{5}+x^{4}-x^{3}+x^{2}-x+\frac{3}{4} \leq 0$ Indication Discuter les cas $x \geq 1, x \leq 0$ et $0<x<1$ .

1 (a) Expand $7(2 x+7)$ (b) Factorise $3 y+12$
2 (a) Expand $5 a(a-6)$ (b) Solve $4(b+2)=24$
3 (a) Factorise fully $12 m+8 m^{2}$ (b) Solve $3(n-5)=27$

$\frac{15 x^{7}-11 x^{6}+25 x^{5}-20 x^{4}}{-5 x^{4}}=$ (Simplify your answer.)

Factor the following expression by grouping. $5 x^{2}-15 x y+2 x y-6 y^{2}$