Polynomials

Problem 2001

Answer the questions about the following polynomial. $-\frac{1}{6}-7 x-9 x^{4}+x^{3}$
Answer Attempt 1 out of 2
The expression represents a $\square$ polynomial with $\square$ terms. The constant term is $\square$ , the leading term is $\square$ , and the leading coefficient is $\square$ .

See Solution

Problem 2002

Evaluate the function $g(x)=x^{2}+5 x$ for the given value of $x$ . Simplify your answer. $g(c-2)=$ $\square$

See Solution

Problem 2003

Expand and combine $-3(3 x-4 a 1)-a(2 y+5 x)$

See Solution

Problem 2004

Multiply: (5.6 k j^{8})(-3.25 k^{9})(\frac{1}{4} k^{7} j^{12}) and find: (-5 m n^{3} p^{5})^{2}.

See Solution

Problem 2005

Find the real solutions of the equation $11 x^{3}+15 x^{2}-25 x+7=0$ . Is the solution set empty or not?

See Solution

Problem 2006

Find $(c \cdot d)(x)$ for $c(x)=4x-2$ and $d(x)=x^2+5x$ .

See Solution

Problem 2007

Determine if the function $f(x)=x^{6}+10 x^{4}-11 x^{2}+19$ is even, odd, or neither. Choices: A, B, C, D.

See Solution

Problem 2008

Identify the common factor in the polynomial $2x^{3} - 4x^{2} + x + 1$ .

See Solution

Problem 2009

Find $(f+g)(x)$ for $f(x)=x^{3}-2 x^{2}+1$ and $g(x)=4 x^{3}-5 x+7$ .

See Solution

Problem 2010

Simplify the expression: $10 \cdot 4p + 2p$ .

See Solution

Problem 2011

8. Determine the degree of $g(x) = x^2(x+3)(x+1)$

See Solution

Problem 2012

$\binom{2}{a} = a^2(3-a)$ $f(x) = x^3$ $f(x) = x$ , $g(x) = (3-x)e^x - 3$

See Solution

Problem 2013

For the given functions $f$ and $g$ , find $f \cdot g$ and state its domain.
$f(x) = 4x - 2$ ; $g(x) = 5x + 7$
A. $(f \cdot g)(x) = 9x^2 + 18x + 5$ ; all real numbers
B. $(f \cdot g)(x) = 20x^2 - 3x - 14$ ; $\{x | x \neq -14 \}$
C. $(f \cdot g)(x) = 20x^2 - 14$ ; $\{x | x \neq -14 \}$
D. $(f \cdot g)(x) = 20x^2 + 18x - 14$ ; all real numbers

See Solution

Problem 2014

$Q(x) + \frac{R(x)}{D(x)}$
$\frac{2x^4 + 7x^2 + 9x - 6}{x^2 - x + 2} =$
$Q(x) + \frac{R(x)}{D(x)} =$

See Solution

Problem 2015

Simplify the expression: $2x - 3x + 2x - 8 + 6 + 7$ .

See Solution

Problem 2016

Evaluate when $c=1$ and $d=3$ : $3(2c+d)-4(c-d)+d^{2}=[?]$

See Solution

Problem 2017

Is the function $g(x)=3 x^{2}-4^{x}+8$ a polynomial? If yes, what is its degree?

See Solution

Problem 2018

Factor the trinomial.
$50 + 15x^2 + x^4$
$x^2(x^2 + 15) + 50$
Suggested tutorial: Learn ... Factor trinomials ... Your answer is incorrect
Need Help? Read It Watch It

See Solution

Problem 2019

$\left(0.4 k^{3}-2.5 k\right)-\left(2.4 k^{3}+3 k^{2}-1.2 k\right)=$ $-2.8 k^{3}-3 k^{2}-3.7 k$ $-2.8 k^{3}+3 k^{2}-1.3 k$ $-2 k^{3}-3 k^{2}-1.3 k$ $-2 k^{3}+3 k^{2}-3.7 k$

See Solution

Problem 2020

History Bookmarks Profiles Tab Window Help BG-249 Wishlist - E Christams scuffers.co dgenuity com/player/
Addition and Subtraction of Polynomials (S Assignment Active
Interpreting the Closure Property
Explain what the following statement means: Polynomials are closed under the operations of addition and subtraction. Provide one addition example and one subtraction example to demonstrate. DONE

See Solution

Problem 2021

Find all zeros of $f(x) = x^3 - 4x^2 + 3x + 2$ . Enter the zeros separated by commas. Enter exact value, not decimal approximations.

See Solution

Problem 2022

Exercice 1 (c) .35 min 07 pt
On considère les polynômes $\boldsymbol{P}$ et $\boldsymbol{Q}$ définis par: $P(x)=-x^{3}-6 x^{2}+9 x+14 \text { et } Q(x)=x^{4}-5 x^{2}+4$
1. a) Vérifier que $(-1)$ est une racine de $P$ . b) Factoriser alors $P(x)$ . c) Résoudre dans $\mathbb{R}$ l'équation $P(x)=0$
En déduire l'ensemble des solutions dans IR de l'équation $x \sqrt{x}-6 x-9 \sqrt{x}+14=0$ b) a) Factoriser le trinôme $T(x)=x^{2}-5 x+4$ . c) En déduire une factorisation du polynôme $Q(x)$ . b) Résoudre dans $\mathbb{R}$ l'équation $\sqrt{Q(x)}=2$ d) Soit $f(x)=\frac{P(x)-Q(x)}{x^{2}+2 x+5}$ a/ Déterminer le domaine de définition de $f$ . b/ Montrer que $f(x)=-x^{2}+x+2$ et vérifier que $f(x)-f(x+1)=2 x$ c/ En déduire la somme $S_{n}=1+2+3+\cdots+n$ où n est un entier naturel supérieur à 2 .

See Solution

Problem 2023

12. Find the sum of the expressions $(11.8t - 1.9)$ and $(-7t + 6.5)$ .

See Solution

Problem 2024

What are the zeros, the degree, and the $y$ -intercept of the polynomial $f(x) = 3x(x + 1)^2(x - 2)^2$ Degree: Zeros: Y-intercept:

See Solution

Problem 2025

14) $10 x y-15 x^{2} y^{2}$

See Solution

Problem 2026

Select the correct answer.
What is the completely factored form of this expression? $3 x^{2}-17 x-28$ A. $(3 x+4)(x+7)$ B. $(3 x+4)(x-7)$ C. $3 x^{2}-17 x-28$ D. $\left(3 x^{2}+4\right)(x-7)$

See Solution

Problem 2027

c. $4x^2 + 24x + 36$

See Solution

Problem 2028

Consider the following. $f(x)=x^{4}-3 x^{2}-4$
Find all the zeros of the function. (Enter your answers as a comma-separated li $x=$ $\square$

See Solution

Problem 2029

Factor the binomial completely. $27-m^{3}$

See Solution

Problem 2030

10. $(7x + 3) - (x + 9)$

See Solution

Problem 2031

8. Factor completely. (a) $3x^2 - x - 14$ (b) $20x^2 + 11x - 3$ (c) $6x^2 + 17x + 12$ (d) $12x^2 - 11x + 2$

See Solution

Problem 2032

In Exercises 1-4, decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient.
1. $f(x)=4 x^{2}-3 x+5 x^{3}-7$
2. $h(x)=5 x^{3}-7 x^{-2}+x-1$
3. $g(x)=x^{4}-\frac{1}{3} x^{2}+10-4 x^{3}+2 x$
4. $f(x)=8 x^{2}-\sqrt{3} x+2$
In Exercises 5-7, evaluate the function for the given value of $x$ .
5. $f(x)=-2 x^{4}+x^{3}+5 x^{2}-3 x-7 ; x=-1$
6. $g(x)=5 x^{4}-2 x^{3}+9 x-10 ; x=-6$
7. $h(x)=x^{5}-4 x^{3}+3 x^{2}+11 x-8 x=7$
In Exercises 8 and 9 , describe the end behavior of the graph of the function.
8. $g(x)=6 x^{4}-3 x^{3}+12 x^{2}+8 x+2$
9. $h(x)=-5 x^{3}+6 x^{2}-5 x^{4}+x^{2}-1$
In Exercises 10-13, graph the polynomial function.
10. $q(x)=x^{4}-2$
11. $h(x)=x^{3}-2 x+3$
12. $k(x)=2 x^{2}+3=x^{3}$
13. $f(x)=x^{3}-2 x^{3}+1$
In Exercises 14 and 16, describe the x-values for which $f$ is inereasing, decreasing, positive, and negative. 14. 16.
16. Suppose $f(x) \rightarrow-\infty$ as $x \rightarrow-\infty$ and $f(x) \Rightarrow-\infty$ as $x \rightarrow+\infty$ . Describe the degree and leading coefficient of the function.

See Solution

Problem 2033

In Exercises 8-11, find the product.
8. $5 x^{2}\left(3 x^{2}+7 x+6\right)$
9. $-2 x^{4}\left(10 x^{3}-9 x^{2}-7 x+4\right)$ $15 x^{4}+35^{3}+30 x^{2}$
10. $\left(8 x^{2}-3 x+1\right)(-3 x+2)$
11. $(-x-6)\left(3 x^{2}+2 x+9\right)$

See Solution

Problem 2034

$-4x + 2x^2 - 5x^4$
$20x^7 + 7 + 18x^6$
$-18x^{24} - 18x^{18} + 9x^{17}$
25 points possible 16/25 answered
Question 17
For the following polynomials, identify the degree, the leading term, and the leading coefficient.
degree leading term leading coefficient
Add Work
Next Question

See Solution

Problem 2035

Find all zeros of $f(x)=x^{3}-4 x^{2}-5 x+14$ . Enter the zeros separated by commas. Enter exact value, not decimal approximations.

See Solution

Problem 2036

Solve for all real values of $y$ in the equation $y^{5}-18 y^{4}+6 y^{3}=0$ .

See Solution

Problem 2037

Find all real solutions for the equation: $y^{5}-16 y^{4}+52 y^{3}=0$ . What are the values of $y$ ?

See Solution

Problem 2038

What level of differences in the sequence $1, 2, \ldots, n$ is constant based on the sum formula $\frac{n(n+1)}{2}$ ?

See Solution

Problem 2039

Find the product of the polynomials $(2 x^{3}+3 x^{2})(4 x^{4}-5 x^{3}-6 x^{2})$ .

See Solution

Problem 2040

Calculate the product of $(2q^9 + 3q^7)(-6q^2 + 9)$ . What is the result?

See Solution

Problem 2041

Use long division to find which polynomial divides evenly by $x+3$ :
1. $x^{3}-5 x^{2}+10 x-15$
2. $x^{3}-3 x^{2}-13 x+15$
3. $3 x^{2}-6 x+9$
4. $5 x^{2}+7 x-12$

See Solution

Problem 2042

Use long division to find which polynomial divides evenly by $x+3$ :
1. $x^{3}-5 x^{2}+10 x-15$
2. $x^{3}-3 x^{2}-13 x+15$
3. $3 x^{2}-6 x+9$
4. $5 x^{2}+7 x-12$

See Solution

Problem 2043

Rewrite $x^{2}-196$ using the identity $x^{2}-a^{2}=(x+a)(x-a)$ . Which polynomial is established?

See Solution

Problem 2044

Which polynomial approximates $\frac{(4 x^{3}+5)(3 x^{6}-8 x^{2})}{2 x^{2}+8 x-4}+4 x^{3}-2 x+13$ ? Options: $12 x^{7}-27$ , $6 x^{7}+15$ , $6 x^{7}+13$ , $6 x^{7}-7$ .

See Solution

Problem 2045

Find the third term in the expansion of $(a+5)^{5}$ using Pascal's Triangle.

See Solution

Problem 2046

Find a term in the expansion of $(a+b)^{7}$ using the Binomial Theorem. Options include $21 a^{6} b$ , $21 a^{2} b^{4}$ , $21 a^{2} b^{5}$ , $a^{4} b^{3}$ .

See Solution

Problem 2047

Find a Pythagorean triple using $\left(11^{2}+4^{2}\right)^{2}=\left(11^{2}-4^{2}\right)^{2}+(2 \cdot 11 \cdot 4)^{2}$ . Which value is in the triple?

See Solution

Problem 2048

Find the second term in the expansion of $(2x - 3)^{6}$ using the Binomial Theorem.

See Solution

Problem 2049

Construct a polynomial for a sequence with constant 4th differences of 48. (4 points)

See Solution

Problem 2050

Find the extra linear factors of $x^{3}-6 x^{2}+11 x-6$ given that $x-3$ is a factor.

See Solution

Problem 2051

How to find the $x$ -intercepts of a polynomial function without graphing? Options: Find zeros, terms, degree, or value at $x=0$ .

See Solution

Problem 2052

Find the multiplicities of the factors in $h(x)=(x+4)(x-1)^{2}(x+3)^{5}$ .

See Solution

Problem 2053

Construct a polynomial function with zeros at $x=4$ (multiplicity 1) and $x=-2$ (multiplicity 3).

See Solution

Problem 2054

What multiplicity does a zero have if the graph touches the $x$ -axis and turns back? Options: 0, 1, 2, 3.

See Solution

Problem 2055

If $(2x+3)$ is a factor of $p(x)$ , what could be its multiplicity? Options: 1, -1.5, 1.5, 2.

See Solution

Problem 2056

Solve the inequality $f(x) \geq 0$ for $f(x)=(x+1)(x-3)^{2}$ using its graph. Provide the solution in interval notation.

See Solution

Problem 2057

Solve the inequality $x^{3}+10 x^{2}>0$ and express the solution in interval notation.

See Solution

Problem 2058

Solve the inequality $x^{3}+7 x^{2}<0$ . Provide the solution in interval notation.

See Solution

Problem 2059

Expand $-3a(b + 2c - 4d)$ .

See Solution

Problem 2060

Write a polynomial function in standard form with real coefficients whose zeros include 2, $8i$ , and $-8i$ .
A polynomial function with zeros 2, $8i$ , and $-8i$ is $f(x) = x^3 - \Box x^2 + \Box x - \Box$ .

See Solution

Problem 2061

1. Multiply the following binomials. Simplify where possible. $\text { a. } \begin{aligned} & (3-x)(12-x) \\ & (3)(12)+(3)(-x)+(-x)(12)+(-x)(-x)= \\ = & 36-3 x-12 x+x= \\ = & 36-14 x \end{aligned}$ b. $(9 a b-6 b)(14 b+3 a)$

See Solution

Problem 2062

Question 68
Find all zeros of $f(x)=x^{3}-7 x^{2}+9 x+$ not decimal approximations.

See Solution

Problem 2063

Match each polynomial expression to its additive inverse. $6x^2 + x - 2$ $-6x^2 - x - 2$ $6x^2 - x + 2$ $-6x^2 + x - 2$ $-6x^2 + x - 2$ $6x^2 - x + 2$ $-6x^2 - x + 2$ $6x^2 + x + 2$

See Solution

Problem 2064

5. List all real solutions for each polynomial function. a) $f(x) = x^3 - 4x^2 - 7x + 10$

See Solution

Problem 2065

5. List all real solutions for each polynomial function. a) $f(x) = x^3 - 4x^2 - 7x + 10$ b) $g(x) = x^3 + 3x^2 - 4x - 12$

See Solution

Problem 2066

10. Which of the following expressions is equivalent to $3.5(4x - 16) + (-2x)$ ? A $14x - 56$ B $12x - 16$ C $14x - 16$ D $12x - 56$

See Solution

Problem 2067

Simplify. $\frac{x^{3}-4 x^{2}+4 x}{x^{3}-2 x^{2}}$

See Solution

Problem 2068

Factor the following trinomial, or state that the trinomial is prime. $p^{2}+18 p-88$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $p^{2}+18 p-88=$ $\square$ (Factor completely.) B. The trinomial is prime.

See Solution

Problem 2069

Factor 6y^7 - y^6 = \text{} (\text{}) Question 1 Question Help: Message instructor Submit Question Jump to Answer

See Solution

Problem 2070

Find the sum. $(-29x^5 + 40x^3 - 40) + (-48x^5 + 70x^3 + 49) =$

See Solution

Problem 2071

What are the roots of the following polynomial: $x^{3}-9 x$ ? $x=0,3$ $x=3$ 的 $x=-3,0$ $x=-3,0,3$ $x=-3,3$

See Solution

Problem 2072

Find the quotient of the polynomial. $\left(2 x^{2}+5 x-12\right) \div(2 x-3)$

See Solution

Problem 2073

$(t-5)(t+5)$

See Solution

Problem 2074

Question What is the y-intercept of the polynomial $f(x)$ defined below? Write the y-value only.
$f(x) = -6 - x^3 - 9x^2 + 3x$
Answer Attempt 1 out of 3 Submit Answer

See Solution

Problem 2075

Find all solutions to the equation $x^{3}+9 x+5 x^{2}=-45$ $-5,-3,3$ $-3,3,5$ $5,-3 i, 3 i$ $-5,-3 i, 3 i$

See Solution

Problem 2076

10) According to the Rational Zero Theorem, list all possible rational roots of $P(x) = \frac{8}{8}x^4 - 3x^2 + 4x - 1$

See Solution

Problem 2077

The polynomial function $B(x) = x^3 + 0x^2 - 21x + 20$ has a known factor of $(x-4)$ . Rewrite $B(x)$ as a product of linear factors.

See Solution

Problem 2078

For the polynomial function $f(x) = x^3 - 2x^2 - 5x + 6$ , we have $f(0) = 6$ , $f(2) = -4$ , $f(3) = 0$ , $f(-1) = 8$ , $f(1) = 0$ . Rewrite $f(x)$ as a product of linear factors. List the values in order from smallest to largest.

See Solution

Problem 2079

Factor. $8 x+16$

See Solution

Problem 2080

$f(x) = -x^5 + 3x^3 - 3x$

See Solution

Problem 2081

Find the GCF of the polynomial $4 x^{4}+12 x^{3}-36 x^{2}+24 x$ . Options: $2 x$ , $6 x$ , 4, $4 x$ .

See Solution

Problem 2082

Find another factor of $x^{3}-5 x^{2}+6 x$ if one factor is linear. Options: $x+3$ , $x-2$ , $x+2$ , $x^{2}+5 x+6$ .

See Solution

Problem 2083

Find the complete set of solutions for $3 x^{3}+9 x^{2}-54 x=0$ : $0,3,-6$ , $0$ , no solutions, or $0,-3,6$ .

See Solution

Problem 2084

Which pattern helps factor $16 x^{8}-49 x^{2}$ ? Options: difference of squares, perfect squares, or neither.

See Solution

Problem 2085

Factor the polynomial $50 x^{5}-32 x=0$ and find the solutions for $x$ .

See Solution

Problem 2086

Solve for $k$ in the equation: $k^{2}-16=6 k^{3}-96 k$ . Provide integer or simplified fraction solutions, separated by commas.

See Solution

Problem 2087

Solve by factoring: $5 x^{3}-10 x^{2}-75 x=0$ . Find all real solutions: $x=$ .

See Solution

Problem 2088

Solve the inequality $(x-3)(x-4)(x-5) \leq 0$ and list intervals with their signs in interval notation.

See Solution

Problem 2089

Solve the inequality $(x-5)(x-6)(x-7) \geq 0$ and list intervals with signs in each interval using interval notation.

See Solution

Problem 2090

Solve the inequality $(x-6)(x-7)(x-8) \geq 0$ and list intervals with signs in interval notation.

See Solution

Problem 2091

Solve the inequality: $(x-4)(x-5)(x-6) \geq 0$ . Provide the solution in interval notation.

See Solution

Problem 2092

Solve the inequality $(x-1)(x-2)(x-3) \geq 0$ and list intervals with signs in each. Use interval notation.

See Solution

Problem 2093

Solve the inequality: $(x-4)(x-5)(x-7) \leq 0$ . Provide the solution in interval notation.

See Solution

Problem 2094

Solve the inequality: $(x-3)(x-4)(x-5) \geq 0$ . List intervals and signs in each interval using interval notation.

See Solution

Problem 2095

Solve the inequality $(x-6)(x-7)(x-8) \geq 0$ and list intervals with signs in interval notation.

See Solution

Problem 2096

Solve the inequality: $(x-2)(x-5)(x-6) \leq 0$ . Provide your answer in interval notation.

See Solution

Problem 2097

Factor the expression $x^{2}-y^{2}$ .

See Solution

Problem 2098

Solve the inequality: $(x-3)(x-4)(x-7) \leq 0$ . Provide the solution in interval notation.

See Solution

Problem 2099

Solve the inequality $x^{3}-x^{2}-90 x>0$ and express the solution in interval notation.

See Solution

Problem 2100

Determine if the function $g(x)=-4 x^{5}+5 x^{3}$ is even, odd, or neither.

See Solution

1 ...18 19 20 21 22 23 24 25

Polynomials

Problem 2001

Problem 2002

Evaluate the function g(x)=x2+5xg(x)=x^{2}+5 xg(x)=x2+5x for the given value of xxx. Simplify your answer. g(c−2)=g(c-2)=g(c−2)= □\square□

Problem 2003

Expand and combine −3(3x−4a1)−a(2y+5x)-3(3 x-4 a 1)-a(2 y+5 x)−3(3x−4a1)−a(2y+5x)

Problem 2004

Multiply: (5.6 k j^{8})(-3.25 k^{9})(\frac{1}{4} k^{7} j^{12}) and find: (-5 m n^{3} p^{5})^{2}.

Problem 2005

Find the real solutions of the equation 11x3+15x2−25x+7=011 x^{3}+15 x^{2}-25 x+7=011x3+15x2−25x+7=0. Is the solution set empty or not?

Problem 2006

Find (c⋅d)(x)(c \cdot d)(x)(c⋅d)(x) for c(x)=4x−2c(x)=4x-2c(x)=4x−2 and d(x)=x2+5xd(x)=x^2+5xd(x)=x2+5x.

Problem 2007

Determine if the function f(x)=x6+10x4−11x2+19f(x)=x^{6}+10 x^{4}-11 x^{2}+19f(x)=x6+10x4−11x2+19 is even, odd, or neither. Choices: A, B, C, D.

Problem 2008

Identify the common factor in the polynomial 2x3−4x2+x+12x^{3} - 4x^{2} + x + 12x3−4x2+x+1.

Problem 2009

Find (f+g)(x)(f+g)(x)(f+g)(x) for f(x)=x3−2x2+1f(x)=x^{3}-2 x^{2}+1f(x)=x3−2x2+1 and g(x)=4x3−5x+7g(x)=4 x^{3}-5 x+7g(x)=4x3−5x+7.

Problem 2010

Simplify the expression: 10⋅4p+2p10 \cdot 4p + 2p10⋅4p+2p.

Problem 2011

8. Determine the degree of g(x)=x2(x+3)(x+1)g(x) = x^2(x+3)(x+1)g(x)=x2(x+3)(x+1)

Problem 2012

(2a)=a2(3−a)\binom{2}{a} = a^2(3-a)(a2​)=a2(3−a) f(x)=x3f(x) = x^3f(x)=x3 f(x)=xf(x) = xf(x)=x, g(x)=(3−x)ex−3g(x) = (3-x)e^x - 3g(x)=(3−x)ex−3

Problem 2013

Problem 2014

Q(x)+R(x)D(x)Q(x) + \frac{R(x)}{D(x)}Q(x)+D(x)R(x)​2x4+7x2+9x−6x2−x+2=\frac{2x^4 + 7x^2 + 9x - 6}{x^2 - x + 2} = x2−x+22x4+7x2+9x−6​=Q(x)+R(x)D(x)=Q(x) + \frac{R(x)}{D(x)} = Q(x)+D(x)R(x)​=

Problem 2015

Simplify the expression: 2x−3x+2x−8+6+72x - 3x + 2x - 8 + 6 + 72x−3x+2x−8+6+7.

Problem 2016

Evaluate when c=1c=1c=1 and d=3d=3d=3: 3(2c+d)−4(c−d)+d2=[?]3(2c+d)-4(c-d)+d^{2}=[?]3(2c+d)−4(c−d)+d2=[?]

Problem 2017

Is the function g(x)=3x2−4x+8g(x)=3 x^{2}-4^{x}+8g(x)=3x2−4x+8 a polynomial? If yes, what is its degree?

Problem 2018

Factor the trinomial.50+15x2+x450 + 15x^2 + x^450+15x2+x4x2(x2+15)+50x^2(x^2 + 15) + 50x2(x2+15)+50Suggested tutorial: Learn ... Factor trinomials ... Your answer is incorrectNeed Help? Read It Watch It

Problem 2019

Problem 2020

Problem 2021

Find all zeros of f(x)=x3−4x2+3x+2f(x) = x^3 - 4x^2 + 3x + 2f(x)=x3−4x2+3x+2. Enter the zeros separated by commas. Enter exact value, not decimal approximations.

Problem 2022

Problem 2023

12. Find the sum of the expressions (11.8t−1.9) (11.8t - 1.9) (11.8t−1.9) and (−7t+6.5) (-7t + 6.5) (−7t+6.5).

Problem 2024

What are the zeros, the degree, and the yyy-intercept of the polynomial f(x)=3x(x+1)2(x−2)2f(x) = 3x(x + 1)^2(x - 2)^2f(x)=3x(x+1)2(x−2)2 Degree: Zeros: Y-intercept:

Problem 2025

14) 10xy−15x2y210 x y-15 x^{2} y^{2}10xy−15x2y2

Problem 2026

Problem 2027

c. 4x2+24x+364x^2 + 24x + 364x2+24x+36

Problem 2028

Consider the following. f(x)=x4−3x2−4f(x)=x^{4}-3 x^{2}-4f(x)=x4−3x2−4Find all the zeros of the function. (Enter your answers as a comma-separated li x=x=x= □\square□

Problem 2029

Factor the binomial completely. 27−m327-m^{3}27−m3

Problem 2030

10. (7x+3)−(x+9) (7x + 3) - (x + 9) (7x+3)−(x+9)

Problem 2031

8. Factor completely. (a) 3x2−x−143x^2 - x - 143x2−x−14 (b) 20x2+11x−320x^2 + 11x - 320x2+11x−3 (c) 6x2+17x+126x^2 + 17x + 126x2+17x+12 (d) 12x2−11x+212x^2 - 11x + 212x2−11x+2

Problem 2032

Problem 2033

Problem 2034

Problem 2035

Find all zeros of f(x)=x3−4x2−5x+14f(x)=x^{3}-4 x^{2}-5 x+14f(x)=x3−4x2−5x+14. Enter the zeros separated by commas. Enter exact value, not decimal approximations.

Problem 2036

Solve for all real values of yyy in the equation y5−18y4+6y3=0y^{5}-18 y^{4}+6 y^{3}=0y5−18y4+6y3=0.

Problem 2037

Find all real solutions for the equation: y5−16y4+52y3=0y^{5}-16 y^{4}+52 y^{3}=0y5−16y4+52y3=0. What are the values of yyy?

Problem 2038

What level of differences in the sequence 1,2,…,n1, 2, \ldots, n1,2,…,n is constant based on the sum formula n(n+1)2\frac{n(n+1)}{2}2n(n+1)​?

Problem 2039

Find the product of the polynomials (2x3+3x2)(4x4−5x3−6x2)(2 x^{3}+3 x^{2})(4 x^{4}-5 x^{3}-6 x^{2})(2x3+3x2)(4x4−5x3−6x2).

Problem 2040

Calculate the product of (2q9+3q7)(−6q2+9)(2q^9 + 3q^7)(-6q^2 + 9)(2q9+3q7)(−6q2+9). What is the result?

Problem 2041

Use long division to find which polynomial divides evenly by x+3x+3x+3: 1. x3−5x2+10x−15x^{3}-5 x^{2}+10 x-15x3−5x2+10x−15 2. x3−3x2−13x+15x^{3}-3 x^{2}-13 x+15x3−3x2−13x+15 3. 3x2−6x+93 x^{2}-6 x+93x2−6x+9 4. 5x2+7x−125 x^{2}+7 x-125x2+7x−12

Problem 2042

Use long division to find which polynomial divides evenly by x+3x+3x+3: 1. x3−5x2+10x−15x^{3}-5 x^{2}+10 x-15x3−5x2+10x−15 2. x3−3x2−13x+15x^{3}-3 x^{2}-13 x+15x3−3x2−13x+15 3. 3x2−6x+93 x^{2}-6 x+93x2−6x+9 4. 5x2+7x−125 x^{2}+7 x-125x2+7x−12

Problem 2043

Rewrite x2−196x^{2}-196x2−196 using the identity x2−a2=(x+a)(x−a)x^{2}-a^{2}=(x+a)(x-a)x2−a2=(x+a)(x−a). Which polynomial is established?

Problem 2044

Which polynomial approximates (4x3+5)(3x6−8x2)2x2+8x−4+4x3−2x+13\frac{(4 x^{3}+5)(3 x^{6}-8 x^{2})}{2 x^{2}+8 x-4}+4 x^{3}-2 x+132x2+8x−4(4x3+5)(3x6−8x2)​+4x3−2x+13? Options: 12x7−2712 x^{7}-2712x7−27, 6x7+156 x^{7}+156x7+15, 6x7+136 x^{7}+136x7+13, 6x7−76 x^{7}-76x7−7.

Evaluate the function $g(x)=x^{2}+5 x$ for the given value of $x$ . Simplify your answer. $g(c-2)=$ $\square$

Expand and combine $-3(3 x-4 a 1)-a(2 y+5 x)$

Find the real solutions of the equation $11 x^{3}+15 x^{2}-25 x+7=0$ . Is the solution set empty or not?

Find $(c \cdot d)(x)$ for $c(x)=4x-2$ and $d(x)=x^2+5x$ .

Determine if the function $f(x)=x^{6}+10 x^{4}-11 x^{2}+19$ is even, odd, or neither. Choices: A, B, C, D.

Identify the common factor in the polynomial $2x^{3} - 4x^{2} + x + 1$ .

Find $(f+g)(x)$ for $f(x)=x^{3}-2 x^{2}+1$ and $g(x)=4 x^{3}-5 x+7$ .

Simplify the expression: $10 \cdot 4p + 2p$ .

8. Determine the degree of $g(x) = x^2(x+3)(x+1)$

$\binom{2}{a} = a^2(3-a)$ $f(x) = x^3$ $f(x) = x$ , $g(x) = (3-x)e^x - 3$

$Q(x) + \frac{R(x)}{D(x)}$
$\frac{2x^4 + 7x^2 + 9x - 6}{x^2 - x + 2} =$
$Q(x) + \frac{R(x)}{D(x)} =$

Simplify the expression: $2x - 3x + 2x - 8 + 6 + 7$ .

Evaluate when $c=1$ and $d=3$ : $3(2c+d)-4(c-d)+d^{2}=[?]$

Is the function $g(x)=3 x^{2}-4^{x}+8$ a polynomial? If yes, what is its degree?

Factor the trinomial.
$50 + 15x^2 + x^4$
$x^2(x^2 + 15) + 50$
Suggested tutorial: Learn ... Factor trinomials ... Your answer is incorrect
Need Help? Read It Watch It

Find all zeros of $f(x) = x^3 - 4x^2 + 3x + 2$ . Enter the zeros separated by commas. Enter exact value, not decimal approximations.

12. Find the sum of the expressions $(11.8t - 1.9)$ and $(-7t + 6.5)$ .

What are the zeros, the degree, and the $y$ -intercept of the polynomial $f(x) = 3x(x + 1)^2(x - 2)^2$ Degree: Zeros: Y-intercept:

14) $10 x y-15 x^{2} y^{2}$

c. $4x^2 + 24x + 36$

Consider the following. $f(x)=x^{4}-3 x^{2}-4$
Find all the zeros of the function. (Enter your answers as a comma-separated li $x=$ $\square$

Factor the binomial completely. $27-m^{3}$

10. $(7x + 3) - (x + 9)$

8. Factor completely. (a) $3x^2 - x - 14$ (b) $20x^2 + 11x - 3$ (c) $6x^2 + 17x + 12$ (d) $12x^2 - 11x + 2$

Find all zeros of $f(x)=x^{3}-4 x^{2}-5 x+14$ . Enter the zeros separated by commas. Enter exact value, not decimal approximations.

Solve for all real values of $y$ in the equation $y^{5}-18 y^{4}+6 y^{3}=0$ .

Find all real solutions for the equation: $y^{5}-16 y^{4}+52 y^{3}=0$ . What are the values of $y$ ?

What level of differences in the sequence $1, 2, \ldots, n$ is constant based on the sum formula $\frac{n(n+1)}{2}$ ?

Find the product of the polynomials $(2 x^{3}+3 x^{2})(4 x^{4}-5 x^{3}-6 x^{2})$ .

Calculate the product of $(2q^9 + 3q^7)(-6q^2 + 9)$ . What is the result?

Use long division to find which polynomial divides evenly by $x+3$ :
1. $x^{3}-5 x^{2}+10 x-15$
2. $x^{3}-3 x^{2}-13 x+15$
3. $3 x^{2}-6 x+9$
4. $5 x^{2}+7 x-12$

Use long division to find which polynomial divides evenly by $x+3$ :
1. $x^{3}-5 x^{2}+10 x-15$
2. $x^{3}-3 x^{2}-13 x+15$
3. $3 x^{2}-6 x+9$
4. $5 x^{2}+7 x-12$

Rewrite $x^{2}-196$ using the identity $x^{2}-a^{2}=(x+a)(x-a)$ . Which polynomial is established?

Which polynomial approximates $\frac{(4 x^{3}+5)(3 x^{6}-8 x^{2})}{2 x^{2}+8 x-4}+4 x^{3}-2 x+13$ ? Options: $12 x^{7}-27$ , $6 x^{7}+15$ , $6 x^{7}+13$ , $6 x^{7}-7$ .

Find the third term in the expansion of $(a+5)^{5}$ using Pascal's Triangle.

Find a term in the expansion of $(a+b)^{7}$ using the Binomial Theorem. Options include $21 a^{6} b$ , $21 a^{2} b^{4}$ , $21 a^{2} b^{5}$ , $a^{4} b^{3}$ .

Find a Pythagorean triple using $\left(11^{2}+4^{2}\right)^{2}=\left(11^{2}-4^{2}\right)^{2}+(2 \cdot 11 \cdot 4)^{2}$ . Which value is in the triple?

Find the second term in the expansion of $(2x - 3)^{6}$ using the Binomial Theorem.

Find the extra linear factors of $x^{3}-6 x^{2}+11 x-6$ given that $x-3$ is a factor.

How to find the $x$ -intercepts of a polynomial function without graphing? Options: Find zeros, terms, degree, or value at $x=0$ .

Find the multiplicities of the factors in $h(x)=(x+4)(x-1)^{2}(x+3)^{5}$ .

Construct a polynomial function with zeros at $x=4$ (multiplicity 1) and $x=-2$ (multiplicity 3).

What multiplicity does a zero have if the graph touches the $x$ -axis and turns back? Options: 0, 1, 2, 3.

If $(2x+3)$ is a factor of $p(x)$ , what could be its multiplicity? Options: 1, -1.5, 1.5, 2.

Solve the inequality $f(x) \geq 0$ for $f(x)=(x+1)(x-3)^{2}$ using its graph. Provide the solution in interval notation.

Solve the inequality $x^{3}+10 x^{2}>0$ and express the solution in interval notation.

Solve the inequality $x^{3}+7 x^{2}<0$ . Provide the solution in interval notation.

Expand $-3a(b + 2c - 4d)$ .

Write a polynomial function in standard form with real coefficients whose zeros include 2, $8i$ , and $-8i$ .
A polynomial function with zeros 2, $8i$ , and $-8i$ is $f(x) = x^3 - \Box x^2 + \Box x - \Box$ .

Question 68
Find all zeros of $f(x)=x^{3}-7 x^{2}+9 x+$ not decimal approximations.

5. List all real solutions for each polynomial function. a) $f(x) = x^3 - 4x^2 - 7x + 10$

5. List all real solutions for each polynomial function. a) $f(x) = x^3 - 4x^2 - 7x + 10$ b) $g(x) = x^3 + 3x^2 - 4x - 12$

10. Which of the following expressions is equivalent to $3.5(4x - 16) + (-2x)$ ? A $14x - 56$ B $12x - 16$ C $14x - 16$ D $12x - 56$

Simplify. $\frac{x^{3}-4 x^{2}+4 x}{x^{3}-2 x^{2}}$

Factor 6y^7 - y^6 = \text{} (\text{}) Question 1 Question Help: Message instructor Submit Question Jump to Answer

Find the sum. $(-29x^5 + 40x^3 - 40) + (-48x^5 + 70x^3 + 49) =$

What are the roots of the following polynomial: $x^{3}-9 x$ ? $x=0,3$ $x=3$ 的 $x=-3,0$ $x=-3,0,3$ $x=-3,3$

Find the quotient of the polynomial. $\left(2 x^{2}+5 x-12\right) \div(2 x-3)$

$(t-5)(t+5)$

Question What is the y-intercept of the polynomial $f(x)$ defined below? Write the y-value only.
$f(x) = -6 - x^3 - 9x^2 + 3x$
Answer Attempt 1 out of 3 Submit Answer