Question 1

Factor the binomial completely.
-$32 a ^ { 4 } b - 18 b ^ { 3 }$

Accepted Answer

A)  $2 b ( 4 a + 3 b ) ^ { 2 }$ 
B)  $2 b ( 4 a - 3 b ) ^ { 2 }$ 
C)  $2 b \left( 4 a ^ { 2 } + 3 b \right) \left( 4 a ^ { 2 } - 3 b \right)$ 
D)  $( 8 a + 6 b ) \left( 4 a b - 3 b ^ { 2 } \right)$ 
A)  $2 b ( 4 a + 3 b ) ^ { 2 }$ 
B)  $2 b ( 4 a - 3 b ) ^ { 2 }$ 
C)  $2 b \left( 4 a ^ { 2 } + 3 b \right) \left( 4 a ^ { 2 } - 3 b \right)$ 
D)  $( 8 a + 6 b ) \left( 4 a b - 3 b ^ { 2 } \right)$

Question 2

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$4 r ^ { 6 } - 8 r ^ { 5 } - 32 r ^ { 4 }$

Accepted Answer

A)  $\left( 4 \mathrm { r } ^ { 3 } + 16 \right) ( \mathrm { r } - 2 )$ 
B)  $4 r ^ { 4 } ( r + 2 ) ( r - 4 )$ 
C)  $4 r ^ { 4 } ( r - 2 ) ( r + 4 )$ 
D)  $\left( 4 \mathrm { r } ^ { 3 } + 8 \right) ( \mathrm { r } - 4 )$ 
A)  $\left( 4 \mathrm { r } ^ { 3 } + 16 \right) ( \mathrm { r } - 2 )$ 
B)  $4 r ^ { 4 } ( r + 2 ) ( r - 4 )$ 
C)  $4 r ^ { 4 } ( r - 2 ) ( r + 4 )$ 
D)  $\left( 4 \mathrm { r } ^ { 3 } + 8 \right) ( \mathrm { r } - 4 )$

Question 3

Factor the binomial completely.
-$36 x ^ { 2 } - 25 y ^ { 2 }$

Accepted Answer

A)  $( 6 x - 5 y ) ^ { 2 }$ 
B)  prime 
C)  $( 6 x + 5 y ) ( 6 x - 5 y )$ 
D)  $( 6 x + 5 y ) ^ { 2 }$ 
A)  $( 6 x - 5 y ) ^ { 2 }$ 
B)  prime 
C)  $( 6 x + 5 y ) ( 6 x - 5 y )$ 
D)  $( 6 x + 5 y ) ^ { 2 }$

Question 4

Factor the four-term polynomial by grouping.
-$3 x - 33 + x y - 11 y$

Accepted Answer

A)  $( y - 11 ) ( 3 x + y )$ 
B)  $( x - 11 y ) ( 3 + y )$ 
C)  $( y - 11 ) ( x + 3 )$ 
D)  $( x - 11 ) ( 3 + y )$ 
A)  $( y - 11 ) ( 3 x + y )$ 
B)  $( x - 11 y ) ( 3 + y )$ 
C)  $( y - 11 ) ( x + 3 )$ 
D)  $( x - 11 ) ( 3 + y )$

Question 5

Factor the sum or difference of two cubes.
-$16 \mathrm { k } ^ { 3 } \mathrm {~m} - 54 \mathrm {~m} ^ { 4 }$

Accepted Answer

A)  $2 m ( 2 k - 3 m ) \left( 4 k ^ { 2 } + 6 k m + 9 m ^ { 2 } \right)$ 
B)  $2 \mathrm {~m} ( 8 \mathrm { k } - 3 \mathrm {~m} ) \left( \mathrm { k } ^ { 2 } + 6 \mathrm {~km} + 9 \mathrm {~m} ^ { 2 } \right)$ 
C)  $\left( 4 k m - 6 m ^ { 2 } \right) \left( 4 k ^ { 2 } + 9 m ^ { 2 } \right)$ 
D)  $2 m \left( 2 k + 3 m ^ { 2 } \right) \left( 4 k ^ { 2 } - 6 k m + 9 k ^ { 2 } \right)$ 
A)  $2 m ( 2 k - 3 m ) \left( 4 k ^ { 2 } + 6 k m + 9 m ^ { 2 } \right)$ 
B)  $2 \mathrm {~m} ( 8 \mathrm { k } - 3 \mathrm {~m} ) \left( \mathrm { k } ^ { 2 } + 6 \mathrm {~km} + 9 \mathrm {~m} ^ { 2 } \right)$ 
C)  $\left( 4 k m - 6 m ^ { 2 } \right) \left( 4 k ^ { 2 } + 9 m ^ { 2 } \right)$ 
D)  $2 m \left( 2 k + 3 m ^ { 2 } \right) \left( 4 k ^ { 2 } - 6 k m + 9 k ^ { 2 } \right)$

Question 6

Solve.
-One leg of a right triangle is 28 inches longer than the smaller leg, and the hypotenuse is 32 inches longer than the smaller leg. Find the lengths of the sides of the triangle.

Accepted Answer

A)  legs: 20 in., 48 in., hypotenuse: 52 in. 
B)  legs: 19 in., 47 in., hypotenuse: 53 in. 
C)  legs: 21 in., 49 in., hypotenuse: 53 in. 
D)  legs: 16 in., 44 in., hypotenuse: 48 in. 
A)  legs: 20 in., 48 in., hypotenuse: 52 in. 
B)  legs: 19 in., 47 in., hypotenuse: 53 in. 
C)  legs: 21 in., 49 in., hypotenuse: 53 in. 
D)  legs: 16 in., 44 in., hypotenuse: 48 in.

Question 7

Factor the trinomial by grouping.
-$15 x ^ { 2 } + 22 x + 8$

Accepted Answer

A)  $( 15 x + 2 ) ( x + 4 )$ 
B)  prime 
C)  $( 3 x + 2 ) ( 5 x + 4 )$ 
D)  $( 3 x - 2 ) ( 5 x - 4 )$ 
A)  $( 15 x + 2 ) ( x + 4 )$ 
B)  prime 
C)  $( 3 x + 2 ) ( 5 x + 4 )$ 
D)  $( 3 x - 2 ) ( 5 x - 4 )$

Question 8

Factor the perfect square trinomial completely.
-$64 y ^ { 2 } - 16 x y + x ^ { 2 }$

Accepted Answer

A)  $( x - 8 y ) ^ { 2 }$ 
B)  prime 
C)  $( x + 8 y ) ^ { 2 }$ 
D)  $( x - 8 y ) ( x + 8 y )$ 
A)  $( x - 8 y ) ^ { 2 }$ 
B)  prime 
C)  $( x + 8 y ) ^ { 2 }$ 
D)  $( x - 8 y ) ( x + 8 y )$

Question 9

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$x ^ { 12 } - 5 x ^ { 6 } + 6$

Accepted Answer

A)  $\left( x ^ { 6 } - 3 \right) ( x - 2 )$ 
B)  $\left( x ^ { 12 } - 3 \right) ( x - 2 )$ 
C)  $\left( x ^ { 6 } - 3 \right) \left( x ^ { 6 } + 2 \right)$ 
D)  $\left( x ^ { 6 } - 3 \right) \left( x ^ { 6 } - 2 \right)$ 
A)  $\left( x ^ { 6 } - 3 \right) ( x - 2 )$ 
B)  $\left( x ^ { 12 } - 3 \right) ( x - 2 )$ 
C)  $\left( x ^ { 6 } - 3 \right) \left( x ^ { 6 } + 2 \right)$ 
D)  $\left( x ^ { 6 } - 3 \right) \left( x ^ { 6 } - 2 \right)$

Question 10

Factor completely.
-$3 x ^ { 2 } + 11 x - 4$

Accepted Answer

A)  $( 3 x + 1 ) ( x - 4 )$ 
B)  $( 3 x - 1 ) ( x + 4 )$ 
C)  $( 3 x - 4 ) ( x + 1 )$ 
D)  $( 3 x + 4 ) ( x - 1 )$ 
A)  $( 3 x + 1 ) ( x - 4 )$ 
B)  $( 3 x - 1 ) ( x + 4 )$ 
C)  $( 3 x - 4 ) ( x + 1 )$ 
D)  $( 3 x + 4 ) ( x - 1 )$

Question 11

Solve the equation.
-$4 x ^ { 2 } + 21 = 20 x$

Accepted Answer

A)  $- \frac { 7 } { 2 } , - \frac { 3 } { 2 }$ 
B)  $\frac { 7 } { 2 } , \frac { 3 } { 2 }$ 
C)  $\frac { 3 } { 4 } , \frac { 9 } { 2 }$ 
D)  $\frac { 7 } { 4 } , \frac { 3 } { 4 }$ 
A)  $- \frac { 7 } { 2 } , - \frac { 3 } { 2 }$ 
B)  $\frac { 7 } { 2 } , \frac { 3 } { 2 }$ 
C)  $\frac { 3 } { 4 } , \frac { 9 } { 2 }$ 
D)  $\frac { 7 } { 4 } , \frac { 3 } { 4 }$

Question 12

Find the GCF for the list.
-$88 x ^ { 3 } , 44 x ^ { 8 }$

Accepted Answer

A)  $88 x ^ { 3 }$ 
B)  $22 x ^ { 5 }$ 
C)  $66 x ^ { 5 }$ 
D)  $44 x ^ { 3 }$ 
A)  $88 x ^ { 3 }$ 
B)  $22 x ^ { 5 }$ 
C)  $66 x ^ { 5 }$ 
D)  $44 x ^ { 3 }$

Question 13

Represent each given condition using a single variable, x.
-The base and height of a triangle whose height is seven less than two times its base.

Accepted Answer

A)  base = x; height = 7x - 2 
B)  height = x; base = 7x - 2 
C)  base = x; height = 2x - 7 
D)  height = x; base = 2x - 7 
A)  base = x; height = 7x - 2 
B)  height = x; base = 7x - 2 
C)  base = x; height = 2x - 7 
D)  height = x; base = 2x - 7

Question 14

Fill in the blank with one of the words or phrases listed below. Not all choices will be used and some choices may be
used more than once. $$\begin{array} { l l l l } 
\text { factoring } & \text { quadratic equation } & \text { perfect square trinomial } & 0 \
\text { greatest common factor } & \text { hypotenuse } & \text { sum of two cubes } & 1 \
\text { difference of two cubes } & \text { difference of two squares } & \text { triangle } & \text { leg }
\end{array}$$
-The Pythagorean theorem states that (leg $) ^ { 2 } + ( \mathrm { leg } ) ^ { 2 } = ($ ____)$^ { 2 }$.

Accepted Answer

A)  quadratic equation 
B)  hypotenuse 
C)  triangle 
D)  leg 
A)  quadratic equation 
B)  hypotenuse 
C)  triangle 
D)  leg

Question 15

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$3 x ^ { 2 } - 21 x + 36$

Accepted Answer

A)  $( x - 3 ) ( 3 x - 12 )$ 
B)  $3 ( x - 12 ) ( x + 1 )$ 
C)  $3 ( x - 3 ) ( x - 4 )$ 
D)  prime 
A)  $( x - 3 ) ( 3 x - 12 )$ 
B)  $3 ( x - 12 ) ( x + 1 )$ 
C)  $3 ( x - 3 ) ( x - 4 )$ 
D)  prime

Question 16

Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$216 x ^ { 3 } - 1$

Accepted Answer

A)  $( 6 x - 1 ) \left( 36 x ^ { 2 } + 6 x + 1 \right)$ 
B)  $( 6 x - 1 ) \left( 36 x ^ { 2 } + 1 \right)$ 
C)  $( 6 x + 1 ) \left( 36 x ^ { 2 } - 6 x + 1 \right)$ 
D)  $( 216 x - 1 ) \left( x ^ { 2 } + 6 x + 1 \right)$ 
A)  $( 6 x - 1 ) \left( 36 x ^ { 2 } + 6 x + 1 \right)$ 
B)  $( 6 x - 1 ) \left( 36 x ^ { 2 } + 1 \right)$ 
C)  $( 6 x + 1 ) \left( 36 x ^ { 2 } - 6 x + 1 \right)$ 
D)  $( 216 x - 1 ) \left( x ^ { 2 } + 6 x + 1 \right)$

Question 17

Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$x ^ { 2 } + 36$

Accepted Answer

A)  $( x + 6 ) ( x - 6 )$ 
B)  $( x - 6 ) ^ { 2 }$ 
C)  $( x + 6 ) ^ { 2 }$ 
D)  prime 
A)  $( x + 6 ) ( x - 6 )$ 
B)  $( x - 6 ) ^ { 2 }$ 
C)  $( x + 6 ) ^ { 2 }$ 
D)  prime

Question 18

Factor the perfect square trinomial completely.
-$x ^ { 2 } + 30 x + 225$

Accepted Answer

A)  $( x - 15 ) ^ { 2 }$ 
B)  $( x + 15 ) ^ { 2 }$ 
C)  $( x + 15 ) ( x - 15 )$ 
D)  prime 
A)  $( x - 15 ) ^ { 2 }$ 
B)  $( x + 15 ) ^ { 2 }$ 
C)  $( x + 15 ) ( x - 15 )$ 
D)  prime

Question 19

Fill in the blank with one of the words or phrases listed below. Not all choices will be used and some choices may be
used more than once. $$\begin{array} { l l l l } 
\text { factoring } & \text { quadratic equation } & \text { perfect square trinomial } & 0 \
\text { greatest common factor } & \text { hypotenuse } & \text { sum of two cubes } & 1 \
\text { difference of two cubes } & \text { difference of two squares } & \text { triangle } & \text { leg }
\end{array}$$
-In a right triangle, each side adjacent to the right angle is called a ________

Accepted Answer

A)  triangle 
B)  hypotenuse 
C)  leg 
D)  quadratic equation 
A)  triangle 
B)  hypotenuse 
C)  leg 
D)  quadratic equation

Question 20

Solve the equation.
-$x ^ { 2 } - 2 x = 24$

Accepted Answer

A)  $- 6,1$ 
B)  6,4 
C)  $- 6,4$ 
D)  $6 , - 4$ 
A)  $- 6,1$ 
B)  6,4 
C)  $- 6,4$ 
D)  $6 , - 4$

Factor the binomial completely. - $32 a ^ { 4 } b - 18 b ^ { 3 }$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $4 r ^ { 6 } - 8 r ^ { 5 } - 32 r ^ { 4 }$

Factor the binomial completely. - $36 x ^ { 2 } - 25 y ^ { 2 }$

Factor the four-term polynomial by grouping. - $3 x - 33 + x y - 11 y$

Factor the sum or difference of two cubes. - $16 \mathrm { k } ^ { 3 } \mathrm {~m} - 54 \mathrm {~m} ^ { 4 }$

Solve. -One leg of a right triangle is 28 inches longer than the smaller leg, and the hypotenuse is 32 inches longer than the smaller leg. Find the lengths of the sides of the triangle.

Factor the trinomial by grouping. - $15 x ^ { 2 } + 22 x + 8$

Factor the perfect square trinomial completely. - $64 y ^ { 2 } - 16 x y + x ^ { 2 }$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $x ^ { 12 } - 5 x ^ { 6 } + 6$

Factor completely. - $3 x ^ { 2 } + 11 x - 4$

Solve the equation. - $4 x ^ { 2 } + 21 = 20 x$

Find the GCF for the list. - $88 x ^ { 3 } , 44 x ^ { 8 }$

Represent each given condition using a single variable, x. -The base and height of a triangle whose height is seven less than two times its base.

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $3 x ^ { 2 } - 21 x + 36$

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $216 x ^ { 3 } - 1$

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $x ^ { 2 } + 36$

Factor the perfect square trinomial completely. - $x ^ { 2 } + 30 x + 225$

Solve the equation. - $x ^ { 2 } - 2 x = 24$

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 6: Factoring Polynomials

Factor the binomial completely. - 32a4b−18b332 a ^ { 4 } b - 18 b ^ { 3 }32a4b−18b3

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - 4r6−8r5−32r44 r ^ { 6 } - 8 r ^ { 5 } - 32 r ^ { 4 }4r6−8r5−32r4

Factor the binomial completely. - 36x2−25y236 x ^ { 2 } - 25 y ^ { 2 }36x2−25y2

Factor the four-term polynomial by grouping. - 3x−33+xy−11y3 x - 33 + x y - 11 y3x−33+xy−11y

Factor the sum or difference of two cubes. - 16k3 m−54 m416 \mathrm { k } ^ { 3 } \mathrm {~m} - 54 \mathrm {~m} ^ { 4 }16k3 m−54 m4