Question 1

Use a special product pattern to find the product $\left( 9 x ^ { 2 } + 8 \right) \left( 9 x ^ { 2 } - 8 \right)$ .

Accepted Answer

A)  $81 x ^ { 2 } - 64$ 
B)  $81 x ^ { 2 } - 72 x + 64$ 
C)  $81 x ^ { 4 } - 144 x ^ { 2 } + 64$ 
D)  $81 x ^ { 4 } - 17 x ^ { 2 } - 64$ 
E)  $81 x ^ { 4 } - 64$ 
A)  $81 x ^ { 2 } - 64$ 
B)  $81 x ^ { 2 } - 72 x + 64$ 
C)  $81 x ^ { 4 } - 144 x ^ { 2 } + 64$ 
D)  $81 x ^ { 4 } - 17 x ^ { 2 } - 64$ 
E)  $81 x ^ { 4 } - 64$

Question 2

Solve the equation below by factoring. $- 14 + 13 x - 3 x ^ { 2 } = 0$

Accepted Answer

A)  $x = - \frac { 7 } { 3 }$ and $x = 2$ 
B)  $x = - 2$ and $x = 0$ 
C)  $x = 0$ and $x = 2$ 
D)  $x = \frac { 7 } { 3 }$ and $x = 2$ 
E)  $x = \frac { 7 } { 3 }$ and $x = - 2$ 
A)  $x = - \frac { 7 } { 3 }$ and $x = 2$ 
B)  $x = - 2$ and $x = 0$ 
C)  $x = 0$ and $x = 2$ 
D)  $x = \frac { 7 } { 3 }$ and $x = 2$ 
E)  $x = \frac { 7 } { 3 }$ and $x = - 2$

Question 3

Is the polynomial below a monomial, binomial, trinomial, or none of these? $4 x ^ { 3 }$

Accepted Answer

A) binomial 
B) monomial 
C) none of these 
D) trinomial 
A) binomial 
B) monomial 
C) none of these 
D) trinomial

Question 4

A closed rectangular box has dimensions of length n inches, width n+4  inches, and height n+6 inches. What is the volume if the shortest side is 7 inches long?

Accepted Answer

A) 189 cubic inches 
B) 495 cubic inches 
C) 320 cubic inches 
D) 96 cubic inches 
E) 1001 cubic inches 
A) 189 cubic inches 
B) 495 cubic inches 
C) 320 cubic inches 
D) 96 cubic inches 
E) 1001 cubic inches

Question 5

Find the difference of the polynomials. $\begin{array} { l } 
x ^ { 4 } + 7 x ^ { 3 } + 5 x - 7 \
- \left( - 3 x ^ { 3 } + 2 x + 7 \right)\
\hline
\end{array}$

Accepted Answer

A)  $x ^ { 4 } + 10 x ^ { 3 } + 3 x - 14$ 
B)  $x ^ { 4 } + 10 x ^ { 3 } + 7 x - 14$ 
C)  $x ^ { 4 } + 10 x ^ { 3 } + 3 x + 14$ 
D)  $x ^ { 4 } + 4 x ^ { 3 } + 3 x + 14$ 
E)  $x ^ { 4 } + 4 x ^ { 3 } + 7 x + 14$ 
A)  $x ^ { 4 } + 10 x ^ { 3 } + 3 x - 14$ 
B)  $x ^ { 4 } + 10 x ^ { 3 } + 7 x - 14$ 
C)  $x ^ { 4 } + 10 x ^ { 3 } + 3 x + 14$ 
D)  $x ^ { 4 } + 4 x ^ { 3 } + 3 x + 14$ 
E)  $x ^ { 4 } + 4 x ^ { 3 } + 7 x + 14$

Question 6

Factor out the greatest common monomial factor from the polynomial $60 t ^ { 2 } - 75$.

Accepted Answer

A)  $15 t ( 4 t - 75 )$ 
B)  $75 \left( 60 t ^ { 2 } - 1 \right)$ 
C)  $60 t ( t - 75 )$ 
D)  $15 \left( 4 t ^ { 2 } - 5 \right)$ 
E) no common factor other than 1 
A)  $15 t ( 4 t - 75 )$ 
B)  $75 \left( 60 t ^ { 2 } - 1 \right)$ 
C)  $60 t ( t - 75 )$ 
D)  $15 \left( 4 t ^ { 2 } - 5 \right)$ 
E) no common factor other than 1

Question 7

Simplify the expression $\frac { 5 ^ { 6 } u ^ { 9 } v ^ { 9 } } { 5 ^ { 8 } u ^ { 9 } v ^ { 3 } }$ . Assume that neither u nor v is zero.

Accepted Answer

A)  $\frac { u v ^ { 6 } } { 10 }$ 
B)  $\frac { v ^ { 6 } } { 25 }$ 
C)  $\frac { v ^ { 6 } } { 10 }$ 
D)  $\frac { v ^ { 3 } } { 25 }$ 
E)  $\frac { u v ^ { 3 } } { 10 }$ 
A)  $\frac { u v ^ { 6 } } { 10 }$ 
B)  $\frac { v ^ { 6 } } { 25 }$ 
C)  $\frac { v ^ { 6 } } { 10 }$ 
D)  $\frac { v ^ { 3 } } { 25 }$ 
E)  $\frac { u v ^ { 3 } } { 10 }$

Question 8

Find the difference $\left( - 6 x ^ { 2 } + 4 x - 12 \right) - \left( 4 x ^ { 3 } + 2 x ^ { 2 } - 12 \right)$ .

Accepted Answer

A)  $- 4 x ^ { 3 } - 8 x ^ { 2 } + 4 x$ 
B)  $- 4 x ^ { 3 } - 4 x ^ { 2 } + 4 x$ 
C)  $- 10 x ^ { 3 } + 2 x ^ { 2 } - 24$ 
D)  $- 10 x ^ { 3 } + 2 x ^ { 2 }$ 
E)  $- 4 x ^ { 3 } - 4 x ^ { 2 } - 24$ 
A)  $- 4 x ^ { 3 } - 8 x ^ { 2 } + 4 x$ 
B)  $- 4 x ^ { 3 } - 4 x ^ { 2 } + 4 x$ 
C)  $- 10 x ^ { 3 } + 2 x ^ { 2 } - 24$ 
D)  $- 10 x ^ { 3 } + 2 x ^ { 2 }$ 
E)  $- 4 x ^ { 3 } - 4 x ^ { 2 } - 24$

Question 9

Factor out the greatest common monomial factor of the polynomial below, if one exists. $20 x ^ { 5 } y ^ { 3 } - 14 x y ^ { 2 } + 8 y ^ { 2 }$

Accepted Answer

A)  $2 y ^ { 2 } \left( 10 x ^ { 5 } y - 7 x + 4 \right)$ 
B)  $2 y ^ { 2 } x \left( 10 x ^ { 4 } y - 7 x + 4 \right)$ 
C)  $y ^ { 2 } \left( 20 x ^ { 5 } y - 14 x + 8 \right)$ 
D)  $2 y ^ { 2 } \left( 10 x ^ { 5 } y ^ { 2 } - 7 x y + 4 y \right)$ 
E) no common factor other than 1 
A)  $2 y ^ { 2 } \left( 10 x ^ { 5 } y - 7 x + 4 \right)$ 
B)  $2 y ^ { 2 } x \left( 10 x ^ { 4 } y - 7 x + 4 \right)$ 
C)  $y ^ { 2 } \left( 20 x ^ { 5 } y - 14 x + 8 \right)$ 
D)  $2 y ^ { 2 } \left( 10 x ^ { 5 } y ^ { 2 } - 7 x y + 4 y \right)$ 
E) no common factor other than 1

Question 10

Simplify the expression. Assume that all variables represent positive integers. $\left( x ^ { y + 5 } \right) ^ { y - 5 }$

Accepted Answer

A)  $x ^ { y^ { 2 } - s ^ { 2 } }$ 
B)  $x ^ { y ^ { 2 } + 2 y 5 + 5 ^ { 2 } }$ 
C)  $x ^ { y ^ { 2 } + s ^ { 2 } }$ 
D)  $x ^ { y ^ { 2 } - 2y5 - 5 ^ { 2 } }$ 
E)  $x ^ { y ^ { 2 } + 2y5 - 5 ^ { 2 } }$ 
A)  $x ^ { y^ { 2 } - s ^ { 2 } }$ 
B)  $x ^ { y ^ { 2 } + 2 y 5 + 5 ^ { 2 } }$ 
C)  $x ^ { y ^ { 2 } + s ^ { 2 } }$ 
D)  $x ^ { y ^ { 2 } - 2y5 - 5 ^ { 2 } }$ 
E)  $x ^ { y ^ { 2 } + 2y5 - 5 ^ { 2 } }$

Question 11

Estimate the x -intercept from the graph below and solve for solutions of the polynomial equation when $y = 0$ . $$y = x ^ { 3 } - x ^ { 2 } - 4 x + 4$$

Accepted Answer

A)  $y = 0$ when x is equal to $- 2,1 \text {, and } 2$ 
B)  $y = 0$ when x is equal to $- 2 , - 1 \text { and } 2$ 
C)  $y = 0$ when x is equal to $- 1,1 \text {, and } 2$ 
D)  $y = 0$ when x is equal to $- 1 \text { and } 1$ 
E)  $y = 0$ when x is equal to $- 2,1 \text {, and } 0$ 
A)  $y = 0$ when x is equal to $- 2,1 \text {, and } 2$ 
B)  $y = 0$ when x is equal to $- 2 , - 1 \text { and } 2$ 
C)  $y = 0$ when x is equal to $- 1,1 \text {, and } 2$ 
D)  $y = 0$ when x is equal to $- 1 \text { and } 1$ 
E)  $y = 0$ when x is equal to $- 2,1 \text {, and } 0$

Question 12

Use the rules of exponents to simplify the expression below. 
$\left[ \frac { \left( 3 x ^ { 2 } \right) ( 3 x ) ^ { 2 } } { \left( - 3 x ^ { 2 } \right) ( 3 x ) } \right] ^ { 3 }$

Accepted Answer

A)  $- 26 x ^ { 7 }$ 
B)  $- 28 x ^ { 3 }$ 
C)  $- 27 x ^ { 3 }$ 
D)  $- 37 x ^ { 6 }$ 
E)  $- 17 x ^ { 8 }$ 
A)  $- 26 x ^ { 7 }$ 
B)  $- 28 x ^ { 3 }$ 
C)  $- 27 x ^ { 3 }$ 
D)  $- 37 x ^ { 6 }$ 
E)  $- 17 x ^ { 8 }$

Question 13

Factor the polynomial $7 x ^ { 3 } - 14 x ^ { 2 } y + 2 x y ^ { 2 } - 4 y ^ { 3 }$ by grouping.

Accepted Answer

A)  $( 7 x - y ) \left( x - 4 y ^ { 3 } \right)$ 
B)  $( 7 x - y ) \left( x + 4 y ^ { 3 } \right)$ 
C)  $( x - 2 y ) \left( 7 x ^ { 2 } - 2 y ^ { 2 } \right)$ 
D)  $( x - 2 y ) \left( 7 x ^ { 2 } + 2 y ^ { 2 } \right)$ 
E)  $( x - 14 y ) \left( 7 x ^ { 2 } - 4 y ^ { 2 } \right)$ 
A)  $( 7 x - y ) \left( x - 4 y ^ { 3 } \right)$ 
B)  $( 7 x - y ) \left( x + 4 y ^ { 3 } \right)$ 
C)  $( x - 2 y ) \left( 7 x ^ { 2 } - 2 y ^ { 2 } \right)$ 
D)  $( x - 2 y ) \left( 7 x ^ { 2 } + 2 y ^ { 2 } \right)$ 
E)  $( x - 14 y ) \left( 7 x ^ { 2 } - 4 y ^ { 2 } \right)$

Question 14

Expand $( x - 3 ) ^ { 3 }$ and simplify.

Accepted Answer

A)  $x ^ { 3 } - 27$ 
B)  $x ^ { 3 } - 9 x ^ { 2 } + 27 x - 27$ 
C)  $x ^ { 3 } + 27 x ^ { 2 } - 9 x - 27$ 
D)  $x ^ { 3 } - 27 x ^ { 2 } + 9 x - 27$ 
E)  $x ^ { 3 } - 3 x ^ { 2 } + 9 x - 27$ 
A)  $x ^ { 3 } - 27$ 
B)  $x ^ { 3 } - 9 x ^ { 2 } + 27 x - 27$ 
C)  $x ^ { 3 } + 27 x ^ { 2 } - 9 x - 27$ 
D)  $x ^ { 3 } - 27 x ^ { 2 } + 9 x - 27$ 
E)  $x ^ { 3 } - 3 x ^ { 2 } + 9 x - 27$

Question 15

Factor the trinomial, if possible. $10 x ^ { 2 } + 47 x y + 42 y ^ { 2 }$

Accepted Answer

A)  $( 5 x - 6 y ) ( 2 x - 7 y )$ 
B)  $( 5 x - 6 y ) ( 2 x + 7 y )$ 
C)  $( 5 x + 6 y ) ( 2 x - 7 y )$ 
D)  $( 5 x + 6 y ) ( 2 x + 7 y )$ 
E) The trinomial is prime. 
A)  $( 5 x - 6 y ) ( 2 x - 7 y )$ 
B)  $( 5 x - 6 y ) ( 2 x + 7 y )$ 
C)  $( 5 x + 6 y ) ( 2 x - 7 y )$ 
D)  $( 5 x + 6 y ) ( 2 x + 7 y )$ 
E) The trinomial is prime.

Question 16

Factor the trinomial $x ^ { 2 n } - 5 x ^ { n } - 36$ . (Assume that n represents a positive integer.)

Accepted Answer

A)  $\left( x ^ { n } - 9 \right) \left( x ^ { n } - 4 \right)$ 
B)  $\left( x ^ { 2 n } - 9 \right) \left( x ^ { 2 n } + 4 \right)$ 
C)  $\left( x ^ { n } - 9 \right) \left( x ^ { n } + 4 \right)$ 
D)  $\left( x ^ { 2 n } + 9 \right) \left( x ^ { 2 n } - 4 \right)$ 
E)  $\left( x ^ { n } + 9 \right) \left( x ^ { n } - 4 \right)$ 
A)  $\left( x ^ { n } - 9 \right) \left( x ^ { n } - 4 \right)$ 
B)  $\left( x ^ { 2 n } - 9 \right) \left( x ^ { 2 n } + 4 \right)$ 
C)  $\left( x ^ { n } - 9 \right) \left( x ^ { n } + 4 \right)$ 
D)  $\left( x ^ { 2 n } + 9 \right) \left( x ^ { 2 n } - 4 \right)$ 
E)  $\left( x ^ { n } + 9 \right) \left( x ^ { n } - 4 \right)$

Question 17

Simplify the expression $\left( - 9 x ^ { 8 } \right) x ^ { 4 }$ .

Accepted Answer

A)  $- 9 x ^ { 32 }$ 
B)  $- 9 x ^ { 16 }$ 
C)  $9 x ^ { - 12 }$ 
D)  $- 9 x ^ { 12 }$ 
E)  $9 x ^ { - 32 }$ 
A)  $- 9 x ^ { 32 }$ 
B)  $- 9 x ^ { 16 }$ 
C)  $9 x ^ { - 12 }$ 
D)  $- 9 x ^ { 12 }$ 
E)  $9 x ^ { - 32 }$

Question 18

Factor the expression below completely, if possible. $x ^ { 4 } - 81 y ^ { 4 }$

Accepted Answer

A)  $( x + 3 y ) ( x - 3 y ) \left( x ^ { 2 } + 9 y ^ { 2 } \right)$ 
B)  $( x + 3 y ) ^ { 2 } ( x - 3 y ) ^ { 2 }$ 
C)  $( x - 3 y ) ^ { 2 } \left( x ^ { 2 } + 9 y ^ { 2 } \right)$ 
D)  $( x + 3 y ) ^ { 3 } ( x - 3 y )$ 
E) The expression is prime. 
A)  $( x + 3 y ) ( x - 3 y ) \left( x ^ { 2 } + 9 y ^ { 2 } \right)$ 
B)  $( x + 3 y ) ^ { 2 } ( x - 3 y ) ^ { 2 }$ 
C)  $( x - 3 y ) ^ { 2 } \left( x ^ { 2 } + 9 y ^ { 2 } \right)$ 
D)  $( x + 3 y ) ^ { 3 } ( x - 3 y )$ 
E) The expression is prime.

Question 19

Multiply the two polynomials using the FOIL Method. $\left( x + \frac { 1 } { 5 } \right) ( 15 x - 10 )$

Accepted Answer

A)  $15 x ^ { 2 } - 7 x - 2$ 
B)  $15 x ^ { 2 } - 7 x + 2$ 
C)  $15 x ^ { 2 } + 7 x + 2$ 
D)  $15 x ^ { 2 } + 13 x + 2$ 
E)  $15 x ^ { 2 } - 13 x - 2$ 
A)  $15 x ^ { 2 } - 7 x - 2$ 
B)  $15 x ^ { 2 } - 7 x + 2$ 
C)  $15 x ^ { 2 } + 7 x + 2$ 
D)  $15 x ^ { 2 } + 13 x + 2$ 
E)  $15 x ^ { 2 } - 13 x - 2$

Question 20

Find two integers c such that the trinomial $x ^ { 2 } + 8 x + c$ can be factored. (There are many correct answers.)

Accepted Answer

A)  $64,64$ 
B)  -48,12 
C)  64,12 
D)  48,-12 
E)  48,12 
A)  $64,64$ 
B)  -48,12 
C)  64,12 
D)  48,-12 
E)  48,12

Use a special product pattern to find the product $\left( 9 x ^ { 2 } + 8 \right) \left( 9 x ^ { 2 } - 8 \right)$ .

Solve the equation below by factoring. $- 14 + 13 x - 3 x ^ { 2 } = 0$

Is the polynomial below a monomial, binomial, trinomial, or none of these? $4 x ^ { 3 }$

A closed rectangular box has dimensions of length n inches, width n+4 inches, and height n+6 inches. What is the volume if the shortest side is 7 inches long?

Find the difference of the polynomials. +7+5x-7 - -3+2x+7

Factor out the greatest common monomial factor from the polynomial $60 t ^ { 2 } - 75$ .

Simplify the expression $\frac { 5 ^ { 6 } u ^ { 9 } v ^ { 9 } } { 5 ^ { 8 } u ^ { 9 } v ^ { 3 } }$ . Assume that neither u nor v is zero.

Find the difference $\left( - 6 x ^ { 2 } + 4 x - 12 \right) - \left( 4 x ^ { 3 } + 2 x ^ { 2 } - 12 \right)$ .

Factor out the greatest common monomial factor of the polynomial below, if one exists. $20 x ^ { 5 } y ^ { 3 } - 14 x y ^ { 2 } + 8 y ^ { 2 }$

Simplify the expression. Assume that all variables represent positive integers. $\left( x ^ { y + 5 } \right) ^ { y - 5 }$

Estimate the x -intercept from the graph below and solve for solutions of the polynomial equation when $y = 0$ . $y = x ^ { 3 } - x ^ { 2 } - 4 x + 4$ $Estimate the x -intercept from the graph below and solve for solutions of the polynomial equation when y = 0 . y = x ^ { 3 } - x ^ { 2 } - 4 x + 4$

Use the rules of exponents to simplify the expression below. $\left[ \frac { \left( 3 x ^ { 2 } \right) ( 3 x ) ^ { 2 } } { \left( - 3 x ^ { 2 } \right) ( 3 x ) } \right] ^ { 3 }$

Factor the polynomial $7 x ^ { 3 } - 14 x ^ { 2 } y + 2 x y ^ { 2 } - 4 y ^ { 3 }$ by grouping.

Expand $( x - 3 ) ^ { 3 }$ and simplify.

Factor the trinomial, if possible. $10 x ^ { 2 } + 47 x y + 42 y ^ { 2 }$

Factor the trinomial $x ^ { 2 n } - 5 x ^ { n } - 36$ . (Assume that n represents a positive integer.)

Simplify the expression $\left( - 9 x ^ { 8 } \right) x ^ { 4 }$ .

Factor the expression below completely, if possible. $x ^ { 4 } - 81 y ^ { 4 }$

Multiply the two polynomials using the FOIL Method. $\left( x + \frac { 1 } { 5 } \right) ( 15 x - 10 )$

Find two integers c such that the trinomial $x ^ { 2 } + 8 x + c$ can be factored. (There are many correct answers.)

Fundamentals of Algebra

Linear Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Rational Expressions, Equations, and Functions

Radicals and Complex Numbers

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conics

Sequences, Series, and the Binomial Theorem

Filters

Exam 5: Polynomials and Factoring

Use a special product pattern to find the product (9x2+8)(9x2−8)\left( 9 x ^ { 2 } + 8 \right) \left( 9 x ^ { 2 } - 8 \right)(9x2+8)(9x2−8) .

Solve the equation below by factoring. −14+13x−3x2=0- 14 + 13 x - 3 x ^ { 2 } = 0−14+13x−3x2=0

Is the polynomial below a monomial, binomial, trinomial, or none of these? 4x34 x ^ { 3 }4x3

A closed rectangular box has dimensions of length n inches, width n+4 inches, and height n+6 inches. What is the volume if the shortest side is 7 inches long?

Find the difference of the polynomials. +7+5x-7 - -3+2x+7

Factor out the greatest common monomial factor from the polynomial 60t2−7560 t ^ { 2 } - 7560t2−75 .

Simplify the expression 56u9v958u9v3\frac { 5 ^ { 6 } u ^ { 9 } v ^ { 9 } } { 5 ^ { 8 } u ^ { 9 } v ^ { 3 } }58u9v356u9v9​ . Assume that neither u nor v is zero.

Find the difference (−6x2+4x−12)−(4x3+2x2−12)\left( - 6 x ^ { 2 } + 4 x - 12 \right) - \left( 4 x ^ { 3 } + 2 x ^ { 2 } - 12 \right)(−6x2+4x−12)−(4x3+2x2−12) .

Factor out the greatest common monomial factor of the polynomial below, if one exists. 20x5y3−14xy2+8y220 x ^ { 5 } y ^ { 3 } - 14 x y ^ { 2 } + 8 y ^ { 2 }20x5y3−14xy2+8y2

Simplify the expression. Assume that all variables represent positive integers. (xy+5)y−5\left( x ^ { y + 5 } \right) ^ { y - 5 }(xy+5)y−5

Estimate the x -intercept from the graph below and solve for solutions of the polynomial equation when y=0y = 0y=0 . y=x3−x2−4x+4y = x ^ { 3 } - x ^ { 2 } - 4 x + 4y=x3−x2−4x+4

Use the rules of exponents to simplify the expression below. [(3x2)(3x)2(−3x2)(3x)]3\left[ \frac { \left( 3 x ^ { 2 } \right) ( 3 x ) ^ { 2 } } { \left( - 3 x ^ { 2 } \right) ( 3 x ) } \right] ^ { 3 }[(−3x2)(3x)(3x2)(3x)2​]3

Factor the polynomial 7x3−14x2y+2xy2−4y37 x ^ { 3 } - 14 x ^ { 2 } y + 2 x y ^ { 2 } - 4 y ^ { 3 }7x3−14x2y+2xy2−4y3 by grouping.

Expand (x−3)3( x - 3 ) ^ { 3 }(x−3)3 and simplify.

Factor the trinomial, if possible. 10x2+47xy+42y210 x ^ { 2 } + 47 x y + 42 y ^ { 2 }10x2+47xy+42y2

Factor the trinomial x2n−5xn−36x ^ { 2 n } - 5 x ^ { n } - 36x2n−5xn−36 . (Assume that n represents a positive integer.)

Simplify the expression (−9x8)x4\left( - 9 x ^ { 8 } \right) x ^ { 4 }(−9x8)x4 .

Factor the expression below completely, if possible. x4−81y4x ^ { 4 } - 81 y ^ { 4 }x4−81y4

Multiply the two polynomials using the FOIL Method. (x+15)(15x−10)\left( x + \frac { 1 } { 5 } \right) ( 15 x - 10 )(x+51​)(15x−10)

Find two integers c such that the trinomial x2+8x+cx ^ { 2 } + 8 x + cx2+8x+c can be factored. (There are many correct answers.)

Fundamentals of Algebra

Linear Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Rational Expressions, Equations, and Functions

Radicals and Complex Numbers

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conics

Sequences, Series, and the Binomial Theorem

Filters

Use a special product pattern to find the product $\left( 9 x ^ { 2 } + 8 \right) \left( 9 x ^ { 2 } - 8 \right)$ .

Solve the equation below by factoring. $- 14 + 13 x - 3 x ^ { 2 } = 0$

Is the polynomial below a monomial, binomial, trinomial, or none of these? $4 x ^ { 3 }$

Factor out the greatest common monomial factor from the polynomial $60 t ^ { 2 } - 75$ .

Simplify the expression $\frac { 5 ^ { 6 } u ^ { 9 } v ^ { 9 } } { 5 ^ { 8 } u ^ { 9 } v ^ { 3 } }$ . Assume that neither u nor v is zero.

Find the difference $\left( - 6 x ^ { 2 } + 4 x - 12 \right) - \left( 4 x ^ { 3 } + 2 x ^ { 2 } - 12 \right)$ .

Factor out the greatest common monomial factor of the polynomial below, if one exists. $20 x ^ { 5 } y ^ { 3 } - 14 x y ^ { 2 } + 8 y ^ { 2 }$

Simplify the expression. Assume that all variables represent positive integers. $\left( x ^ { y + 5 } \right) ^ { y - 5 }$

Estimate the x -intercept from the graph below and solve for solutions of the polynomial equation when $y = 0$ . $y = x ^ { 3 } - x ^ { 2 } - 4 x + 4$ $Estimate the x -intercept from the graph below and solve for solutions of the polynomial equation when y = 0 . y = x ^ { 3 } - x ^ { 2 } - 4 x + 4$

Use the rules of exponents to simplify the expression below. $\left[ \frac { \left( 3 x ^ { 2 } \right) ( 3 x ) ^ { 2 } } { \left( - 3 x ^ { 2 } \right) ( 3 x ) } \right] ^ { 3 }$

Factor the polynomial $7 x ^ { 3 } - 14 x ^ { 2 } y + 2 x y ^ { 2 } - 4 y ^ { 3 }$ by grouping.

Expand $( x - 3 ) ^ { 3 }$ and simplify.

Factor the trinomial, if possible. $10 x ^ { 2 } + 47 x y + 42 y ^ { 2 }$

Factor the trinomial $x ^ { 2 n } - 5 x ^ { n } - 36$ . (Assume that n represents a positive integer.)

Simplify the expression $\left( - 9 x ^ { 8 } \right) x ^ { 4 }$ .

Factor the expression below completely, if possible. $x ^ { 4 } - 81 y ^ { 4 }$

Multiply the two polynomials using the FOIL Method. $\left( x + \frac { 1 } { 5 } \right) ( 15 x - 10 )$

Find two integers c such that the trinomial $x ^ { 2 } + 8 x + c$ can be factored. (There are many correct answers.)