Polynomials

Problem 1101

For the polynomial function $f(x)=3(x-9)(x+6)^{2}$ answer the following questions. (a) List each real zero and its multiplicity. (b) Determine whether the graph crosses or touches the x -axis at each x -intercept. (c) Determine the maximum number of turning points on the graph. (d) Determine the end behavior; that is, find the power function that the graph of $f$ resembles for large values of $|x|$ . (a) Find any real zeros of f . Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The real zero of $f$ is $\square$ with multiplicity $\square$ . (Type an exact answer, $u$ The smallest zero of $f$ is B. The smallest zero of $f$ is $\square$ with multiplicity $\square$ . The largest zero of $f$ is $\square$ with multiplicity $\square$ . (Type an exact answer, using radicals as needed. Type integers or fractions.) C. The smallest zero of $f$ is $\square$ with multiplicity $\square$ . The middle zero of $f$ is $\square$ with multiplicity $\square$ . The largest zero of $f$ is (Type an exact answer, using radicals as needed. Type integers or fractions.) $\square$ with multiplicity $\qquad$ . D. There are no real zeros. (b) Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The graph crosses the $x$ -axis at $\square$ . B. The graph touches the $x$ -axis at
$\square$ . (Type an exact answer, using radic The graph touches the $x$ -axis at
$\square$ C. The graph touches the $x$ -axis at $\square$ and crosses at $\square$ . (Type an exact answer, using radicals as needed. Type integers or simplified fractions. Use a comma to separate answers as needed.) D. The graph neither crosses nor touches the $x$ -axis.

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Problem 1102

14) $x^{4}-16$

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Problem 1103

14) $x^{4}-16$

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Problem 1104

15) $9 p^{2} r+73 p r+70 r$

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Problem 1105

Evaluate $x^{2} y + w$ for $w = -17$ , $x = 4$ , and $y = 6$ .

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Problem 1106

Simplify: (2+√10)(7+√10). Choose one: a. 14+2√10 b. 24+9√10 c. 14+9√10 d. 114+9√10

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Problem 1107

What is the complete factorization of $81 w^{8}-36 w^{4}$ ? Choose the correct option.

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Problem 1108

Find the factored form of $x^{3}+343$ . Choose from: a. $(x+7)^{3}$ , b. $(x+7)(x^{2}+49)$ , c. $(x+7)(x^{2}+7x+49)$ , d. $(x+7)(x^{2}-7x+49)$ .

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Problem 1109

Find the polynomial for which $(2 y-3)$ is a factor: a. $12 y-8$ , b. $45 y^{2}-20$ , c. $16 y^{3}-54$ , d. $2 y^{2}+y-3$ .

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Problem 1110

Find the solution for $x$ in the equation $x^{3}-64=0$ . Choose from the options: a. $x=-4$ , b. $x=-8$ , c. $x=-2+2 i \sqrt{3}$ , d. $x=-2+2 \sqrt{3}$ .

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Problem 1111

Identify the value that is not a solution to the equation $x^{3}+7x-9x-63=0$ . Options: a. 9, b. -7, c. 3, d. -3.

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Problem 1112

Find a polynomial with zeros at -4 (multiplicity 3), -1 (multiplicity 8), and 2 (multiplicity 1). What is its equation?

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Problem 1113

A polynomial has a zero at $x=4 i$ . Which expression is a factor? a. $(x^{2}+8)$ b. $(x^{2}-8)$ c. $(x^{2}+16)$ d. $(x^{2}-16)$

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Problem 1114

Divide the polynomial $x^{3}+9 x^{2}+32 x+48$ by $x+4$ using synthetic division.

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Problem 1115

Find the difference: (3 - 3n²) - (2n² - 4). What is the simplified expression?

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Problem 1116

Find the sum of $4n^4 - 1$ and $4n^3 - 2$ . What is the result?

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Problem 1117

Simplify the sum: $(-12 n^{3}+8 n^{2}+5 n^{4})+(9 n^{3}-14 n^{2}+6 n^{4})$

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Problem 1118

Simplify the expression: $(-1 - 4x^3 - 12x^2) - (11 + 13x^3 + 6x^2)$ .

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Problem 1119

Find the product of (x-3) and (2x² + 3x - 1).

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Problem 1120

Simplify the expression: $(x - 6x^2 + 3x^3 - 8x^4) + (2x + 3x^4 - 8x^3 - 5x^2)$ .

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Problem 1121

Simplify the expression using the fewest terms: $(4 x^{2}+10 y^{2}-2 x)+(7 x^{2}+3 y^{2}-2 x)-(12 x^{2}+9 y^{2}-x)$ .

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Problem 1122

Distribute and simplify using the box method: $(-3x + 3)(2x - 1)$ .

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Problem 1123

Expand the expression $(2x - 4y + c)^{2}$ .

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Problem 1124

Simplify the expression: $8a - 6 + a - 1$ .

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Problem 1125

Combine like terms in the expression: $7x - 2x^{2} + 3 - x^{2}$ .

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Problem 1126

Combine like terms in the expression: $-x + 5y^{2} - 4 - 2y^{2} - 2x + 3$ .

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Problem 1127

Problem 1. [Recognizing polynomials] Consider the following functions. Which are polynomials? What are their respective degrees? Which functions are you unsure about and why? (a) $y=3^{x}+9^{x}+5$ (d) $y=4$ (b) $y=x^{2}+5 x+3 x^{3}+\pi+56$ (e) $y=\sqrt{x}+\sqrt[3]{x^{2}}+2$ (c) $y=x\left(x^{2}-3\right)$ (f) $y=(2 x-3)^{2}(x+4)$
Important Features of Polynomials

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Problem 1128

Determine whether the given statement is true or false if $k=2$ . $7 k^{2}-5 k+12 \geq 4 k+23$ The statement is true. The statement is false.

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Problem 1129

$x^{3}+3 x$
What is the most efficient u-substitution? Select only ONE answer. $u=x$ $u=x^{2}$ $u=x^{3}+3 x$ $u=x+1$ $u=x^{3}$

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Problem 1130

The expression given is $5 a b^{4} \cdot 3 c$ . However, to solve an expression, we typically need an equation (something set equal to a value) or additional context, such as values for the variables or a specific variable to solve for. Since the expression is not an equation, it cannot be "solved" in the traditional sense. If you have an equation or additional instructions, please provide them. Otherwise, the expression can be simplified by multiplying the coefficients and combining the variables:
$5 a b^{4} \cdot 3 c = 15 a b^{4} c$

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Problem 1131

Factor by grouping: $x^{2}+10 x+4 x+40$ $\square$ Question Help: ⓐ $V_{i d e}$ Submit question ${ }^{\text {Message instructor }}$

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Problem 1132

For the function $f(x)=10(x+8)^{7}-10$ , find $f^{-1}(x)$ .

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Problem 1133

Find the zeros and multiplicity of the function $f(x) = 5x^3 - 30x^2 + 45x$ .

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Problem 1134

Express the following polynomial function in terms of Legendre Polynomial $f(x)=x^{3}+1$

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Problem 1135

9
The polynomial function $p$ is given by $p(x)=(x+3)\left(x^{2}-2 x-15\right)$ . Which of the following describes the zeros of $p$ ? (A) $p$ has exactly two distinct real zeros. (ib) $p$ has exactly three distinct real zeros. (C) $p$ has exactly one distinct real zero and no non-real zeros. (D) $p$ has exactly one distinct real zero and two non-real zeros.

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Problem 1136

10. 2 Points
The polynomial function $p$ is given by $p(x)=-4 x^{5}+3 x^{2}+1$ . Which of the following statements about the end behavior of $p$ is true? (A) The sign of the leading term of $p$ is positive, and the degree of the leading term of $p$ is even; therefore, $\lim _{x \rightarrow-\infty} p(x)=\infty$ and $\lim _{x \rightarrow \infty} p(x)=\infty$ . (B) The sign of the leading term of $p$ is negative, and the degree of the leading term of $p$ is odd; therefore, $\lim _{x \rightarrow-\infty} p(x)=\infty$ and $\lim _{x \rightarrow \infty} p(x)=-\infty$ . (C) The sign of the leading term of $p$ is positive, and the degree of the leading term of $p$ is odd; therefore, $\lim _{x \rightarrow-\infty} p(x)=-\infty$ and $\lim _{x \rightarrow \infty} p(x)=\infty$ . (D) The sign of the leading term of $p$ is negative, and the degree of the leading term of $p$ is odd; therefore, $\lim _{x \rightarrow-\infty} p(x)=-\infty$ and $\lim _{x \rightarrow \infty} p(x)=\infty$ .

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Problem 1137

NAME $\qquad$ DATE 4.3: Operations with Polynomials Practice dd or subtract.
1. $\left(6 a^{2}+5 a+10\right)-\left(4 a^{2}+6 a+12\right)$ $=2 a^{4}-1 a-2$
2. $(g+5)+(2 g+7)$ $=2 g^{2}+7 g+10 g+35$
3. $\left(x^{2}-3 x-3\right)+\left(2 x^{2}+7 x-2\right)$
4. $(2 x-3)-(5 x-6)$

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Problem 1138

4. [0.31/0.43 Points] DETAILS MY NOTES SCOLALG7 3.5.034.MI. 3/100 Submissions Used PREVIOUS ANSWERS ASK YOUR TEACHE
Factor the polynomial completely. $\begin{array}{r} P(x)=x^{5}+2 x^{3} \\ P(x)=\square \end{array}$ $\begin{array}{l} x=\square \text { with multiplicity } \square \\ x=\square \text { with multiplicity } \square \\ x=\square \text { with multiplicity } \square \end{array}$ Need Help? Read II Whitch it Master It

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Problem 1139

\begin{tabular}{|l|l|} \hline Directions: Find each sum or difference. Answers must be in standard form. \\ \hline 11. $\left(x^{2}-4 x+3\right)+\left(3 x^{2}-3 x-5\right)$ & 12. $\left(8 r^{2}-12 r+4\right)-\left(3 r^{2}+5 r-1\right)$ \\ \hline 13. $\left(2 m-3+7 m^{2}\right)-\left(3-9 m^{2}-2 m\right)$ & 14. $\left(7 p^{2}+3 p\right)-\left(5 p^{2}+4\right)$ \\ \hline 15. $\left(3 a^{2}-a+3\right)+\left(4 a^{2}-5\right)$ & 16. $\left(5 w^{3}-w+2 w^{2}+4\right)+\left(3 w^{2}+1-4 w\right)$ \\ \hline 17. $\left(2 x^{2}+3 y^{2}-z^{2}\right)-\left(x^{2}-y^{2}-z^{2}\right)+\left(4 x^{2}-3 y^{2}\right)$ & \begin{tabular}{l}
18. $\left(12+8 k^{3}+3 k-4 k^{2}\right)+\left(5 k^{3}+15-k+7\right.$ \\ \end{tabular} \\ \hline 19. Find the sum of $\left(2 x^{2}-6 x-2\right)$ and $\left(x^{2}+4 x\right)$ . & \begin{tabular}{l}
20. Subtract $\left(-a^{2}-5 a b+3 b^{2}\right)$ from \\ $\left(3 a^{2}-2 a b+3 b^{2}\right)$ . \end{tabular} \\ & \end{tabular}

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Problem 1140

Pascal's Triangle to expand $\left(3+2 x^{2}\right)^{4}$ . Express your answer in simplest form.

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Problem 1141

Find the 2 nd term in the expansion of $(x+5 y)^{6}$ in simplest form.

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Problem 1142

NAME $\qquad$ DATE $\qquad$ PERIOD $\qquad$
Determine whether each equation is an identity.
5. $(x+3)^{2}\left(x^{3}+3 x^{2}+3 x+1\right)=\left(x^{2}+6 x+9\right)(x+1)^{3}$ $\left.(x+3)^{(x+3}\right)$ $\left(x^{2}+3 x+3 x+9\right)$

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Problem 1143

3. Determine if the function is even, odd, or neither. a. $f(x)=x^{4}-3 x^{2}+2$ . b. $f(x)=x^{3}-7 x+5$ . c. $f(x)=x^{3}-2 x$ .

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Problem 1144

59. $6 d+4(3 d+5)$
62. $a+\frac{a}{5}+\frac{2}{5} a$
65. $7(2 x+y)+6(x+5 y)$

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Problem 1145

Use the rational zeros theorem to list all possible rational zeros of the following. $f(x)=-25 x^{3}-2 x^{2}+4 x-1$
Be sure that no value in your list appears more than once.

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Problem 1146

$(3 x-2)^{2}$

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Problem 1147

How many roots, real or complex, does the polynomial $7+5 x^{4}-3 x^{2}$ have in all?
7 3 4 5

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Problem 1148

Find the degree of this polynomial.

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Problem 1149

Factor the binomial completely. $z^{4}-1$
Part: $0 / 4$ $\square$
Part 1 of 4
The GCF is 1 . $z^{4}-1$ is a difference of squares. Write in the form $a^{2}-b^{2}$ , where $a=z^{2}$ and $b=$ $\square$ .

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Problem 1150

Consider the following polynomial. $h(x)=-8 x^{2}(x+9)(x-1)$
Step 1 of 2: Find the degree and leading coefficient of $\mathrm{h}(\mathrm{x})$ .

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Problem 1151

$\begin{aligned} 4 p^{5}(v-4)(9 v-1) & =4 p^{5}\left(9 v^{2}-v-36 v+4\right) \\ & =4 p^{5}\left(9 v^{2}-\square v+4\right)\end{aligned}$

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Problem 1152

Factor the higher degree polynomial. $x^{4}-2 x^{2}-15$
Part: $0 / 3$
Part 1 of 3
To produce the product $x^{4}$ , we must use $x^{2}$ and $\square$ .

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Problem 1153

Consider the following polynomial inequality. $x^{2}(x+6)(x-3)>0$
Step 1 of 2 : Write the polynomial inequality in the form $p(x)<0, p(x) \leq 0, p(x)>0$ , or $p(x) \geq 0$ ; then find the real zeros of $p(x)$ .

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Problem 1154

Find the value of $x$ when $f(x) = 0$ for the function $f(x) = -2x^3 + 3x^2 + 12x + 2$ .

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Problem 1155

$\frac{5 \pm \sqrt{c}}{2} \quad$ Practice Divide using synthetic division.
14. $\left(x^{2}+20 x+91\right) \div(x+7)$
16. $\left(x^{4}+x^{3}-1\right) \div(x-2)$
18. $\left(3 x^{4}-2 x^{3}+5 x^{2}-4 x-2\right) \div(x+1)$
15. $\left(x^{3}-9 x^{2}+27 x-28\right) \div(x-3)$
17. $\left(x^{4}-8 x^{2}+16\right) \div(x+2)$
19. $\left(2 x^{3}-2 x-3\right) \div(x-1)$

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Problem 1156

Determine the leading term, the leading coefficient, and the degree of the polynomial. Then classify the polynomial as constant, linear, quadratic, cubic, or quartic. $g(x)=-\frac{1}{3} x^{3}-3 x+5$
The leading term of the polynomial is $\square$ (Use integers or fractions for any numbers in the expression.) The leading coefficient of the polynomial is $\square$ (Type an integer or a fraction.) The degree of the polynomtial is $\square$ The polynomial is $\square$

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Problem 1157

2. A) Usando el método de los coeficientes indeterminados, hallar $T(x)$ de tercer grado sabiendo que $T(-2)=-140$ , que $T(0)=-18$ , que una de sus raíces es $x=3$ , y que el coeficiente principal de $T(x)$ es 5 .

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Problem 1158

e. No restrictions; Domain is all real numbers
Clear my choice
Given the following polynomial function, use Descartes Rule of Signs to determine the possible number of positive and negative $f(x)=x^{3}-2 x^{2}-6 x+4$
Number of positive real zeros $\square$ Number of negative real zeros $\square$

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Problem 1159

PRIMERA PARTE:
1. A) Sea $M(x) \equiv(m+k) x^{3}+(3 m-k) x^{2}+3 k x+35$ , hallar $m$ y $k$ sabiendo que $x=-5$ es raíz de $M(x)$ y que $M(-3)=80$ .

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Problem 1160

Consider the following polynomial function. $f(x)=x^{4}+2 x^{3}-13 x^{2}-10 x+40$
Step 2 of 4 : Find the degree and the $y$ -intercept. Express the intercept as an ordered pair.

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Problem 1161

Question 2 of 6, Step 3 of 4 4/15 Correct
Consider the following polynomial function. $f(x)=x^{4}-6 x^{3}+3 x^{2}+30 x-40$
Step 3 of 4 : Find the $x$ -intercept(s) at which $f$ crosses the axis. Express the intercept(s) as ordered pair(s).
Answer
Select the number of $x$ -intercept(s) at which $f$ crosses the axis.
Selecting an option will display any text boxes needed to complete your answer. none 1 2 3 4

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Problem 1162

Consider the following polynomial function. $f(x)=x^{4}+6 x^{3}+x^{2}-42 x-56$
Step 4 of 4: Find the zero(s) at which $f$ "flattens out". Express the zero(s) as ordered pair(s).
Answer
Select the number of zero(s) at which $f$ "flattens out".
Selecting an option will display any text boxes needed to complete your answer. none 1 2 3 4

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Problem 1163

6. Given the polynomial function: $\mathrm{f}(\mathrm{x})=(\mathrm{x}+2)(\mathrm{x}-1)^{2}(\mathrm{x}+2)^{2}$ u. Find the zeros (x-intercepts) v. Find the $y$ -intercept. w . Find the degree and the leading coefficient x. Sketch the graph.

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Problem 1164

Find all zeros of the following polynomial. Be sure to find the appropriate number of solutions (counting multiplicity) using the Linear Factors Theorem. $f(x)=x^{5}+5 x^{4}+23 x^{3}+83 x^{2}+112 x+48$

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Problem 1165

Answer the following questions about the equation below. $12 x^{3}+53 x^{2}-34 x+5=0$ (a) List all rational roots that are possible according to the Rational Zero Theorem. Choose the correct A. $\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 12$ B. $\pm 1, \pm 5, \pm \frac{1}{2}, \pm \frac{5}{2}, \pm \frac{1}{3}, \pm \frac{5}{3}, \pm \frac{1}{4}, \pm \frac{5}{4}, \pm \frac{1}{6}, \pm \frac{5}{6}, \pm \frac{1}{12}, \pm \frac{5}{12}$ C. $\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 12, \pm \frac{1}{5}, \pm \frac{2}{5}, \pm \frac{3}{5}, \pm \frac{4}{5}, \pm \frac{6}{5}, \pm \frac{12}{5}$ D. $\pm 1, \pm 5$ (b) Use synthetic division to test several possible rational roots in order to identify one actual root.
One rational root of the given equation is $\square$ (Simplify your answer.)

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Problem 1166

[文], Simplify the expression: $d-9 d+-2 d+-2 d$ $\square$ Submit

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Problem 1167

Consider the following polynomial function. $f(x)=x^{4}-6 x^{3}+x^{2}+42 x-56$
Step 3 of 4 : Find the $x$ -intercept(s) at which $f$ crosses the axis. Express the intercept(s) as ordered pair(s).
Answer
Select the number of $x$ -intercept(s) at which $f$ crosses the axis.
Selecting an option will display any text boxes needed to complete your answer. none 1 2 3

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Problem 1168

Express your answer as a polynomial in standard form. $\begin{array}{l} f(x)=2 x^{2}-x+6 \\ g(x)=2 x+12 \end{array}$
Find: $g(f(x))$

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Problem 1169

Simplify the expression by combining like terms: $2(3x + 2) + (2y + 1)$ .

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Problem 1170

Simplify the expression: $3\left(x^{2}+5 x+5\right)-\left(x^{2}+3 x+1\right)$ .

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Problem 1171

Simplify the expression: $2(2a - 5) - (a - 3)$ . What is the result?

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Problem 1172

Simplify the expression: $(2 x^{2}-4 x+1)+(5 x+x^{2}-1)$ .

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Problem 1173

Given $f(x)=-3x+2$ and $g(x)=x^2+4x-7$ , find $f(x) \cdot g(x)$ .

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Problem 1174

Given $f(x)=3 x^{2}+4 x+2$ and $g(x)=6 x+1$ , find $f(x) \cdot g(x)$ .

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Problem 1175

Identify equivalent expressions to $4(4 a+5)$ . Select 3: $16 a+5$ , $16 a+20$ , $12 a+20+4 a$ , $2(8 a+10)$ , $16 a+5+4$ .

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Problem 1176

Find the slope from $(3, f(3))$ to $(3+h, f(3+h))$ for $f(x)=x^{2}+9x$ as a function of $h$ .

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Problem 1177

Find the expression equivalent to $4(4 a+6)$ . Options: $16 a+24$ , $4(6 a+4)$ , $24 a+16$ , $16 a+6$ .

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Problem 1178

Find expressions equivalent to $3(5 f+7)+7 f$ . Options include $5(7 f+3)+7 f$ , $7(3 f+5)+7 f$ , $3(4 f+f+7)+7 f$ , and $12 f+21$ .

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Problem 1179

Determine if the function $g(x)=-9 x^{3}+8$ is even, odd, or neither.

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Problem 1180

Determine if $g(x)=x^{3}-48 x$ is even, odd, or neither. Find the local maximum value given a local minimum of -128 at 4.

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Problem 1181

For the function $g(x)=-x^{3}+48 x$ , check if it's even, odd, or neither, and find the local maximum value given a local minimum of -128 at -4.

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Problem 1182

Given the function $F(x)=-x^{4}+2 x^{2}+224$ , find if it's even/odd, a second max value, and the area from $x=-4$ to $x=0$ .

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Problem 1183

Find the least common multiple of $16 u^{3} x^{4}$ and $6 u^{7} v^{5} x^{2}$ .

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Problem 1184

Simplify the expression $a^{2}+2(b-6)-17$ .

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Problem 1185

Find the least common multiple of $16 u^{3} x^{4}$ and $6 u^{7} v^{5} x^{2}$ .

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Problem 1186

Find the least common multiple of $16 u^{3} x^{4}$ and $6 u^{7} v^{5} x^{2}$ .

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Problem 1187

Simplify the expression: $4y - y(3 - 7y) + 5 + 2(8 - y)$ . What should you do first?

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Problem 1188

Given the function $F(x)=-x^{4}+16 x^{2}+225$ , find if it's even/odd, another local max, and area from $x=-5$ to $x=0$ .

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Problem 1189

For the function $F(x)=-x^{4}+4 x^{2}+192$ , find if $F$ is even/odd, a second local max, and area from $x=-4$ to $x=0$ .

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Problem 1190

Simplify: $6y - 4(4z - 3y) + 2z$

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Problem 1191

Find real values of $x$ such that $f(x)=0$ where $f(x)=x^{3}-x$ . Enter answers as a list.

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Problem 1192

Multiply the monomial: $5 x(4 x y)$ . What is the result?

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Problem 1193

Factor the expression $64 - x^{2}$ completely over the integers.

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Problem 1194

Multiply the polynomials $(x-4)(2x-3)$ and express the result in standard form.

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Problem 1195

Multiply the polynomials and write your answer in standard form: $(4)(5)(3 + 5)$

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Problem 1196

Multiply (2 cos x + 1)(3 cos x - 1)

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Problem 1197

Simplify: $4 - \left[\left(4b^{3} - 25b^{2} + 14b - 2\right) \div (4b - 1)\right] - \square b^{2} + b$

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Problem 1198

What is the first step to simplify $11 x - 2 - 3(1 - 7 x)^{2} - (x + 1)$ ?

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Problem 1199

Find the domain of the function $g(x)=\frac{2}{3} x^{2}-\frac{1}{6} \times \frac{3}{4}$ .

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Problem 1200

Simplify the expression: $(4 x^{3}-12 x^{2})+(7 x-21)$ .

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1 ...9 10 11 12 13 14 15 ...25

Polynomials

Problem 1101

Problem 1102

14) x4−16x^{4}-16x4−16

Problem 1103

14) x4−16x^{4}-16x4−16

Problem 1104

15) 9p2r+73pr+70r9 p^{2} r+73 p r+70 r9p2r+73pr+70r

Problem 1105

Evaluate x2y+wx^{2} y + wx2y+w for w=−17w = -17w=−17, x=4x = 4x=4, and y=6y = 6y=6.

Problem 1106

Simplify: (2+√10)(7+√10). Choose one: a. 14+2√10 b. 24+9√10 c. 14+9√10 d. 114+9√10

Problem 1107

What is the complete factorization of 81w8−36w481 w^{8}-36 w^{4}81w8−36w4? Choose the correct option.

Problem 1108

Find the factored form of x3+343x^{3}+343x3+343. Choose from: a. (x+7)3(x+7)^{3}(x+7)3, b. (x+7)(x2+49)(x+7)(x^{2}+49)(x+7)(x2+49), c. (x+7)(x2+7x+49)(x+7)(x^{2}+7x+49)(x+7)(x2+7x+49), d. (x+7)(x2−7x+49)(x+7)(x^{2}-7x+49)(x+7)(x2−7x+49).

Problem 1109

Find the polynomial for which (2y−3)(2 y-3)(2y−3) is a factor: a. 12y−812 y-812y−8, b. 45y2−2045 y^{2}-2045y2−20, c. 16y3−5416 y^{3}-5416y3−54, d. 2y2+y−32 y^{2}+y-32y2+y−3.

Problem 1110

Find the solution for xxx in the equation x3−64=0x^{3}-64=0x3−64=0. Choose from the options: a. x=−4x=-4x=−4, b. x=−8x=-8x=−8, c. x=−2+2i3x=-2+2 i \sqrt{3}x=−2+2i3​, d. x=−2+23x=-2+2 \sqrt{3}x=−2+23​.

Problem 1111

Identify the value that is not a solution to the equation x3+7x−9x−63=0x^{3}+7x-9x-63=0x3+7x−9x−63=0. Options: a. 9, b. -7, c. 3, d. -3.

Problem 1112

Find a polynomial with zeros at -4 (multiplicity 3), -1 (multiplicity 8), and 2 (multiplicity 1). What is its equation?

Problem 1113

A polynomial has a zero at x=4ix=4 ix=4i. Which expression is a factor? a. (x2+8)(x^{2}+8)(x2+8) b. (x2−8)(x^{2}-8)(x2−8) c. (x2+16)(x^{2}+16)(x2+16) d. (x2−16)(x^{2}-16)(x2−16)

Problem 1114

Divide the polynomial x3+9x2+32x+48x^{3}+9 x^{2}+32 x+48x3+9x2+32x+48 by x+4x+4x+4 using synthetic division.

Problem 1115

Find the difference: (3 - 3n²) - (2n² - 4). What is the simplified expression?

Problem 1116

Find the sum of 4n4−14n^4 - 14n4−1 and 4n3−24n^3 - 24n3−2. What is the result?

Problem 1117

Simplify the sum: (−12n3+8n2+5n4)+(9n3−14n2+6n4)(-12 n^{3}+8 n^{2}+5 n^{4})+(9 n^{3}-14 n^{2}+6 n^{4})(−12n3+8n2+5n4)+(9n3−14n2+6n4)

Problem 1118

Simplify the expression: (−1−4x3−12x2)−(11+13x3+6x2)(-1 - 4x^3 - 12x^2) - (11 + 13x^3 + 6x^2)(−1−4x3−12x2)−(11+13x3+6x2).

Problem 1119

Find the product of (x-3) and (2x² + 3x - 1).

Problem 1120

Simplify the expression: (x−6x2+3x3−8x4)+(2x+3x4−8x3−5x2)(x - 6x^2 + 3x^3 - 8x^4) + (2x + 3x^4 - 8x^3 - 5x^2)(x−6x2+3x3−8x4)+(2x+3x4−8x3−5x2).

Problem 1121

Simplify the expression using the fewest terms: (4x2+10y2−2x)+(7x2+3y2−2x)−(12x2+9y2−x)(4 x^{2}+10 y^{2}-2 x)+(7 x^{2}+3 y^{2}-2 x)-(12 x^{2}+9 y^{2}-x)(4x2+10y2−2x)+(7x2+3y2−2x)−(12x2+9y2−x).

Problem 1122

Distribute and simplify using the box method: (−3x+3)(2x−1)(-3x + 3)(2x - 1)(−3x+3)(2x−1).

Problem 1123

Expand the expression (2x−4y+c)2(2x - 4y + c)^{2}(2x−4y+c)2.

Problem 1124

Simplify the expression: 8a−6+a−18a - 6 + a - 18a−6+a−1.

Problem 1125

Combine like terms in the expression: 7x−2x2+3−x2 7x - 2x^{2} + 3 - x^{2} 7x−2x2+3−x2.

Problem 1126

Combine like terms in the expression: −x+5y2−4−2y2−2x+3-x + 5y^{2} - 4 - 2y^{2} - 2x + 3−x+5y2−4−2y2−2x+3.

Problem 1127

Problem 1128

Determine whether the given statement is true or false if k=2k=2k=2. 7k2−5k+12≥4k+237 k^{2}-5 k+12 \geq 4 k+237k2−5k+12≥4k+23 The statement is true. The statement is false.

Problem 1129

x3+3xx^{3}+3 xx3+3xWhat is the most efficient u-substitution? Select only ONE answer. u=xu=xu=x u=x2u=x^{2}u=x2 u=x3+3xu=x^{3}+3 xu=x3+3x u=x+1u=x+1u=x+1 u=x3u=x^{3}u=x3

Problem 1130

Problem 1131

Factor by grouping: x2+10x+4x+40x^{2}+10 x+4 x+40x2+10x+4x+40 □\square□ Question Help: ⓐ VideV_{i d e}Vide​ Submit question Message instructor { }^{\text {Message instructor }}Message instructor

Problem 1132

For the function f(x)=10(x+8)7−10f(x)=10(x+8)^{7}-10f(x)=10(x+8)7−10, find f−1(x)f^{-1}(x)f−1(x).

Problem 1133

Find the zeros and multiplicity of the function f(x)=5x3−30x2+45x f(x) = 5x^3 - 30x^2 + 45x f(x)=5x3−30x2+45x.

Problem 1134

Express the following polynomial function in terms of Legendre Polynomial f(x)=x3+1f(x)=x^{3}+1f(x)=x3+1

Problem 1135

Problem 1136

Problem 1137

Problem 1138

Problem 1139

Problem 1140

Pascal's Triangle to expand (3+2x2)4\left(3+2 x^{2}\right)^{4}(3+2x2)4. Express your answer in simplest form.

Problem 1141

Find the 2 nd term in the expansion of (x+5y)6(x+5 y)^{6}(x+5y)6 in simplest form.

Problem 1142

Problem 1143

3. Determine if the function is even, odd, or neither. a. f(x)=x4−3x2+2f(x)=x^{4}-3 x^{2}+2f(x)=x4−3x2+2. b. f(x)=x3−7x+5f(x)=x^{3}-7 x+5f(x)=x3−7x+5. c. f(x)=x3−2xf(x)=x^{3}-2 xf(x)=x3−2x.

Problem 1144

59. 6d+4(3d+5)6 d+4(3 d+5)6d+4(3d+5)62. a+a5+25aa+\frac{a}{5}+\frac{2}{5} aa+5a​+52​a65. 7(2x+y)+6(x+5y)7(2 x+y)+6(x+5 y)7(2x+y)+6(x+5y)

14) $x^{4}-16$

14) $x^{4}-16$

15) $9 p^{2} r+73 p r+70 r$

Evaluate $x^{2} y + w$ for $w = -17$ , $x = 4$ , and $y = 6$ .

What is the complete factorization of $81 w^{8}-36 w^{4}$ ? Choose the correct option.

Find the factored form of $x^{3}+343$ . Choose from: a. $(x+7)^{3}$ , b. $(x+7)(x^{2}+49)$ , c. $(x+7)(x^{2}+7x+49)$ , d. $(x+7)(x^{2}-7x+49)$ .

Find the polynomial for which $(2 y-3)$ is a factor: a. $12 y-8$ , b. $45 y^{2}-20$ , c. $16 y^{3}-54$ , d. $2 y^{2}+y-3$ .

Find the solution for $x$ in the equation $x^{3}-64=0$ . Choose from the options: a. $x=-4$ , b. $x=-8$ , c. $x=-2+2 i \sqrt{3}$ , d. $x=-2+2 \sqrt{3}$ .

Identify the value that is not a solution to the equation $x^{3}+7x-9x-63=0$ . Options: a. 9, b. -7, c. 3, d. -3.

A polynomial has a zero at $x=4 i$ . Which expression is a factor? a. $(x^{2}+8)$ b. $(x^{2}-8)$ c. $(x^{2}+16)$ d. $(x^{2}-16)$

Divide the polynomial $x^{3}+9 x^{2}+32 x+48$ by $x+4$ using synthetic division.

Find the sum of $4n^4 - 1$ and $4n^3 - 2$ . What is the result?

Simplify the sum: $(-12 n^{3}+8 n^{2}+5 n^{4})+(9 n^{3}-14 n^{2}+6 n^{4})$

Simplify the expression: $(-1 - 4x^3 - 12x^2) - (11 + 13x^3 + 6x^2)$ .

Simplify the expression: $(x - 6x^2 + 3x^3 - 8x^4) + (2x + 3x^4 - 8x^3 - 5x^2)$ .

Simplify the expression using the fewest terms: $(4 x^{2}+10 y^{2}-2 x)+(7 x^{2}+3 y^{2}-2 x)-(12 x^{2}+9 y^{2}-x)$ .

Distribute and simplify using the box method: $(-3x + 3)(2x - 1)$ .

Expand the expression $(2x - 4y + c)^{2}$ .

Simplify the expression: $8a - 6 + a - 1$ .

Combine like terms in the expression: $7x - 2x^{2} + 3 - x^{2}$ .

Combine like terms in the expression: $-x + 5y^{2} - 4 - 2y^{2} - 2x + 3$ .

Determine whether the given statement is true or false if $k=2$ . $7 k^{2}-5 k+12 \geq 4 k+23$ The statement is true. The statement is false.

$x^{3}+3 x$
What is the most efficient u-substitution? Select only ONE answer. $u=x$ $u=x^{2}$ $u=x^{3}+3 x$ $u=x+1$ $u=x^{3}$

Factor by grouping: $x^{2}+10 x+4 x+40$ $\square$ Question Help: ⓐ $V_{i d e}$ Submit question ${ }^{\text {Message instructor }}$

For the function $f(x)=10(x+8)^{7}-10$ , find $f^{-1}(x)$ .

Find the zeros and multiplicity of the function $f(x) = 5x^3 - 30x^2 + 45x$ .

Express the following polynomial function in terms of Legendre Polynomial $f(x)=x^{3}+1$

Pascal's Triangle to expand $\left(3+2 x^{2}\right)^{4}$ . Express your answer in simplest form.

Find the 2 nd term in the expansion of $(x+5 y)^{6}$ in simplest form.

3. Determine if the function is even, odd, or neither. a. $f(x)=x^{4}-3 x^{2}+2$ . b. $f(x)=x^{3}-7 x+5$ . c. $f(x)=x^{3}-2 x$ .

59. $6 d+4(3 d+5)$
62. $a+\frac{a}{5}+\frac{2}{5} a$
65. $7(2 x+y)+6(x+5 y)$

Use the rational zeros theorem to list all possible rational zeros of the following. $f(x)=-25 x^{3}-2 x^{2}+4 x-1$
Be sure that no value in your list appears more than once.

$(3 x-2)^{2}$

How many roots, real or complex, does the polynomial $7+5 x^{4}-3 x^{2}$ have in all?
7 3 4 5

Factor the binomial completely. $z^{4}-1$
Part: $0 / 4$ $\square$
Part 1 of 4
The GCF is 1 . $z^{4}-1$ is a difference of squares. Write in the form $a^{2}-b^{2}$ , where $a=z^{2}$ and $b=$ $\square$ .

Consider the following polynomial. $h(x)=-8 x^{2}(x+9)(x-1)$
Step 1 of 2: Find the degree and leading coefficient of $\mathrm{h}(\mathrm{x})$ .

$\begin{aligned} 4 p^{5}(v-4)(9 v-1) & =4 p^{5}\left(9 v^{2}-v-36 v+4\right) \\ & =4 p^{5}\left(9 v^{2}-\square v+4\right)\end{aligned}$

Factor the higher degree polynomial. $x^{4}-2 x^{2}-15$
Part: $0 / 3$
Part 1 of 3
To produce the product $x^{4}$ , we must use $x^{2}$ and $\square$ .

Consider the following polynomial inequality. $x^{2}(x+6)(x-3)>0$
Step 1 of 2 : Write the polynomial inequality in the form $p(x)<0, p(x) \leq 0, p(x)>0$ , or $p(x) \geq 0$ ; then find the real zeros of $p(x)$ .

Find the value of $x$ when $f(x) = 0$ for the function $f(x) = -2x^3 + 3x^2 + 12x + 2$ .

2. A) Usando el método de los coeficientes indeterminados, hallar $T(x)$ de tercer grado sabiendo que $T(-2)=-140$ , que $T(0)=-18$ , que una de sus raíces es $x=3$ , y que el coeficiente principal de $T(x)$ es 5 .

PRIMERA PARTE:
1. A) Sea $M(x) \equiv(m+k) x^{3}+(3 m-k) x^{2}+3 k x+35$ , hallar $m$ y $k$ sabiendo que $x=-5$ es raíz de $M(x)$ y que $M(-3)=80$ .

Consider the following polynomial function. $f(x)=x^{4}+2 x^{3}-13 x^{2}-10 x+40$
Step 2 of 4 : Find the degree and the $y$ -intercept. Express the intercept as an ordered pair.

6. Given the polynomial function: $\mathrm{f}(\mathrm{x})=(\mathrm{x}+2)(\mathrm{x}-1)^{2}(\mathrm{x}+2)^{2}$ u. Find the zeros (x-intercepts) v. Find the $y$ -intercept. w . Find the degree and the leading coefficient x. Sketch the graph.

Find all zeros of the following polynomial. Be sure to find the appropriate number of solutions (counting multiplicity) using the Linear Factors Theorem. $f(x)=x^{5}+5 x^{4}+23 x^{3}+83 x^{2}+112 x+48$

[文], Simplify the expression: $d-9 d+-2 d+-2 d$ $\square$ Submit

Express your answer as a polynomial in standard form. $\begin{array}{l} f(x)=2 x^{2}-x+6 \\ g(x)=2 x+12 \end{array}$
Find: $g(f(x))$

Simplify the expression by combining like terms: $2(3x + 2) + (2y + 1)$ .

Simplify the expression: $3\left(x^{2}+5 x+5\right)-\left(x^{2}+3 x+1\right)$ .

Simplify the expression: $2(2a - 5) - (a - 3)$ . What is the result?

Simplify the expression: $(2 x^{2}-4 x+1)+(5 x+x^{2}-1)$ .

Given $f(x)=-3x+2$ and $g(x)=x^2+4x-7$ , find $f(x) \cdot g(x)$ .

Given $f(x)=3 x^{2}+4 x+2$ and $g(x)=6 x+1$ , find $f(x) \cdot g(x)$ .