Question 1

Factor the trinomial by grouping.
-$3 x ^ { 2 } + 11 x - 20$

Accepted Answer

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

Question 2

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 ________ of a list of terms is the product of all common factors.

Accepted Answer

A)  difference of two squares 
B)  perfect square trinomial 
C)  greatest common factor 
D)  difference of two cubes 
A)  difference of two squares 
B)  perfect square trinomial 
C)  greatest common factor 
D)  difference of two cubes

Question 3

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$6 x ^ { 2 } - 18 x y - 24 y ^ { 2 }$

Accepted Answer

A)  $6 ( x - y ) ( x + 4 y )$ 
B)  prime 
C)  $( 6 x - 6 y ) ( x + 4 y )$ 
D)  $6 ( x + y ) ( x - 4 y )$ 
A)  $6 ( x - y ) ( x + 4 y )$ 
B)  prime 
C)  $( 6 x - 6 y ) ( x + 4 y )$ 
D)  $6 ( x + y ) ( x - 4 y )$

Question 4

Solve.
-The area of a circle is 144π square meters. Find its radius.

Accepted Answer

A)  11 m 
B)  24 m 
C)  12 m 
D)  72 m 
A)  11 m 
B)  24 m 
C)  12 m 
D)  72 m

Question 5

Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$6 x ^ { 3 } - 60 x ^ { 2 } + 126 x$

Accepted Answer

A)  $6 x ( x + 7 ) ( x + 3 )$ 
B)  $x ( 6 x + 7 ) ( x + 3 )$ 
C)  $6 x ( x - 7 ) ( x - 3 )$ 
D)  $x ( x + 7 ) ( 6 x + 18 )$ 
A)  $6 x ( x + 7 ) ( x + 3 )$ 
B)  $x ( 6 x + 7 ) ( x + 3 )$ 
C)  $6 x ( x - 7 ) ( x - 3 )$ 
D)  $x ( x + 7 ) ( 6 x + 18 )$

Question 6

Factor the four-term polynomial by grouping.
-$8 x ^ { 4 } - 20 x ^ { 2 } + 10 x ^ { 2 } - 25$

Accepted Answer

A)  $\left( 4 x ^ { 2 } + 5 \right) \left( 2 x ^ { 2 } - 5 \right)$ 
B)  $\left( 4 x ^ { 2 } - 5 \right) \left( 2 x ^ { 2 } + 5 \right)$ 
C)  $\left( 8 x ^ { 2 } - 5 \right) \left( x ^ { 2 } + 5 \right)$ 
D)  $\left( 4 x ^ { 4 } + 5 \right) ( 2 x - 5 )$ 
A)  $\left( 4 x ^ { 2 } + 5 \right) \left( 2 x ^ { 2 } - 5 \right)$ 
B)  $\left( 4 x ^ { 2 } - 5 \right) \left( 2 x ^ { 2 } + 5 \right)$ 
C)  $\left( 8 x ^ { 2 } - 5 \right) \left( x ^ { 2 } + 5 \right)$ 
D)  $\left( 4 x ^ { 4 } + 5 \right) ( 2 x - 5 )$

Question 7

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. $$\begin{array} { l l l l } 
\text { factoring } & \text { quadratic equation } & \text { perfect square trinomial } & 0 \
\text { greatest common factor } & \text { hypotenuse } & \text { sum of two cubes } & 1 \
\text { difference of two cubes } & \text { difference of two squares } & \text { triangle } & \text { leg }
\end{array}$$
-An equation that can be written in the form $a x ^ { 2 } + b x + c = 0$ (with a not 0 ) is called a_________

Accepted Answer

A)  perfect square trinomial 
B)  quadratic equation 
C)  difference of two squares 
D)  greatest common factor 
A)  perfect square trinomial 
B)  quadratic equation 
C)  difference of two squares 
D)  greatest common factor

Question 8

Factor the sum or difference of two cubes.
-$t ^ { 3 } + 8$

Accepted Answer

A)  $( t + 2 ) \left( t ^ { 2 } - 2 t + 4 \right)$ 
B)  $( t - 2 ) \left( t ^ { 2 } + 2 t + 4 \right)$ 
C)  $( t - 8 ) ( t + 1 ) ( t - 1 )$ 
D)  $( t + 2 ) \left( t ^ { 2 } + 4 \right)$ 
A)  $( t + 2 ) \left( t ^ { 2 } - 2 t + 4 \right)$ 
B)  $( t - 2 ) \left( t ^ { 2 } + 2 t + 4 \right)$ 
C)  $( t - 8 ) ( t + 1 ) ( t - 1 )$ 
D)  $( t + 2 ) \left( t ^ { 2 } + 4 \right)$

Question 9

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$- x ^ { 2 } - 8 x + 48$

Accepted Answer

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

Question 10

Factor out the GCF from the polynomial.
-$64 x ^ { 8 } y ^ { 9 } + 16 x ^ { 2 } y ^ { 4 } - 72 x ^ { 5 } y ^ { 2 }$

Accepted Answer

A)  $8 x ^ { 2 } y ^ { 2 } \left( 8 x ^ { 6 } y ^ { 7 } + 2 y ^ { 2 } - 9 x ^ { 3 } \right)$ 
B)  $x ^ { 2 } y ^ { 2 } \left( 64 x ^ { 6 } y ^ { 7 } + 16 y ^ { 2 } - 72 x ^ { 3 } \right)$ 
C)  $8 \left( 8 x ^ { 8 } y ^ { 9 } + 2 x ^ { 2 } y ^ { 4 } - 9 x ^ { 5 } y ^ { 2 } \right)$ 
D)  $8 x ^ { 2 } \left( 8 x ^ { 6 } y ^ { 9 } + 2 y ^ { 4 } - 9 x ^ { 3 } y ^ { 2 } \right)$ 
A)  $8 x ^ { 2 } y ^ { 2 } \left( 8 x ^ { 6 } y ^ { 7 } + 2 y ^ { 2 } - 9 x ^ { 3 } \right)$ 
B)  $x ^ { 2 } y ^ { 2 } \left( 64 x ^ { 6 } y ^ { 7 } + 16 y ^ { 2 } - 72 x ^ { 3 } \right)$ 
C)  $8 \left( 8 x ^ { 8 } y ^ { 9 } + 2 x ^ { 2 } y ^ { 4 } - 9 x ^ { 5 } y ^ { 2 } \right)$ 
D)  $8 x ^ { 2 } \left( 8 x ^ { 6 } y ^ { 9 } + 2 y ^ { 4 } - 9 x ^ { 3 } y ^ { 2 } \right)$

Question 11

Solve.
-The side of a square equals the length of a rectangle. The width of the rectangle is 4 meters longer than its length. The sum of the areas of the square and the rectangle is 198 square centimeters.
Find the side of the square.

Accepted Answer

A)  2 cm 
B)  11 cm 
C)  9 cm 
D)  81 cm 
A)  2 cm 
B)  11 cm 
C)  9 cm 
D)  81 cm

Question 12

Factor the sum or difference of two cubes.
-$512 p ^ { 3 + 1 }$

Accepted Answer

A)  $( 8 p + 1 ) \left( 64 p ^ { 2 } - 8 p - 1 \right)$ 
B)  $( 8 p + 1 ) \left( 64 p ^ { 2 } - 8 p + 1 \right)$ 
C)  $( 8 p + 1 ) \left( 64 p ^ { 2 } + 1 \right)$ 
D)  $( 8 p + 1 ) \left( 64 p ^ { 2 } + 8 p + 1 \right)$ 
A)  $( 8 p + 1 ) \left( 64 p ^ { 2 } - 8 p - 1 \right)$ 
B)  $( 8 p + 1 ) \left( 64 p ^ { 2 } - 8 p + 1 \right)$ 
C)  $( 8 p + 1 ) \left( 64 p ^ { 2 } + 1 \right)$ 
D)  $( 8 p + 1 ) \left( 64 p ^ { 2 } + 8 p + 1 \right)$

Question 13

Find the GCF for the list.
-12, 24, 27

Accepted Answer

A)  6 
B)  1 
C)  3 
D)  12 
A)  6 
B)  1 
C)  3 
D)  12

Question 14

Factor completely.
-$10 x ^ { 2 } + 11 x y - 6 y ^ { 2 }$

Accepted Answer

A)  prime 
B)  $( 2 x + 3 y ) ( 5 x - 2 y )$ 
C)  $( 2 x - 3 y ) ( 5 x + 2 y )$ 
D)  $( 10 x + 3 y ) ( x - 2 y )$ 
A)  prime 
B)  $( 2 x + 3 y ) ( 5 x - 2 y )$ 
C)  $( 2 x - 3 y ) ( 5 x + 2 y )$ 
D)  $( 10 x + 3 y ) ( x - 2 y )$

Question 15

Factor out the GCF from the polynomial.
-$10 m ^ { 9 } + 4 m ^ { 6 } + 4 m ^ { 3 }$

Accepted Answer

A)  $2 \left( 5 m ^ { 9 } + 2 m ^ { 6 } + 2 m ^ { 3 } \right)$ 
B)  $m ^ { 3 } \left( 10 m ^ { 6 } + 4 m ^ { 3 } + 4 \right)$ 
C)  $2 m ^ { 3 } \left( 5 m ^ { 6 } + 2 m ^ { 3 } + 2 \right)$ 
D)  $- 2 m ^ { 3 } \left( 5 m ^ { 6 } - 2 m ^ { 3 } - 2 \right)$ 
A)  $2 \left( 5 m ^ { 9 } + 2 m ^ { 6 } + 2 m ^ { 3 } \right)$ 
B)  $m ^ { 3 } \left( 10 m ^ { 6 } + 4 m ^ { 3 } + 4 \right)$ 
C)  $2 m ^ { 3 } \left( 5 m ^ { 6 } + 2 m ^ { 3 } + 2 \right)$ 
D)  $- 2 m ^ { 3 } \left( 5 m ^ { 6 } - 2 m ^ { 3 } - 2 \right)$

Question 16

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. $$\begin{array} { l l l l } 
\text { factoring } & \text { quadratic equation } & \text { perfect square trinomial } & 0 \
\text { greatest common factor } & \text { hypotenuse } & \text { sum of two cubes } & 1 \
\text { difference of two cubes } & \text { difference of two squares } & \text { triangle } & \text { leg }
\end{array}$$
-By the zero factor property, if the product of two numbers is 0, then at least one of the numbers must be ________

Accepted Answer

A)  0 
B)  greatest common factor 
C)  quadratic equation 
D)  1 
A)  0 
B)  greatest common factor 
C)  quadratic equation 
D)  1

Question 17

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

Accepted Answer

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

Question 18

Factor the trinomial by grouping.
-$8 x ^ { 2 } - x - 34$

Accepted Answer

A)  $( 8 x - 17 ) ( x + 2 )$ 
B)  $( 8 x + 17 ) ( x - 2 )$ 
C)  $( 8 x - 2 ) ( x + 17 )$ 
D)  $( 8 x + 2 ) ( x - 17 )$ 
A)  $( 8 x - 17 ) ( x + 2 )$ 
B)  $( 8 x + 17 ) ( x - 2 )$ 
C)  $( 8 x - 2 ) ( x + 17 )$ 
D)  $( 8 x + 2 ) ( x - 17 )$

Question 19

Factor completely.
-$75 x ^ { 3 } - 110 x ^ { 2 } + 40 x$

Accepted Answer

A)  $x ( 15 x - 10 ) ( 5 x - 4 )$ 
B)  $x ( 3 x - 2 ) ( 25 x - 20 )$ 
C)  $5 \left( 3 x ^ { 2 } - 2 \right) ( 5 x - 4 )$ 
D)  $5 x ( 3 x - 2 ) ( 5 x - 4 )$ 
A)  $x ( 15 x - 10 ) ( 5 x - 4 )$ 
B)  $x ( 3 x - 2 ) ( 25 x - 20 )$ 
C)  $5 \left( 3 x ^ { 2 } - 2 \right) ( 5 x - 4 )$ 
D)  $5 x ( 3 x - 2 ) ( 5 x - 4 )$

Question 20

Solve the equation.
-$( x + 8 ) ( x + 1 ) = 44$

Accepted Answer

A)  $- 8 , - 1$ 
B)  1,8 
C)  $- 3,12$ 
D)  $- 12,3$ 
A)  $- 8 , - 1$ 
B)  1,8 
C)  $- 3,12$ 
D)  $- 12,3$

Factor the trinomial by grouping. - $3 x ^ { 2 } + 11 x - 20$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $6 x ^ { 2 } - 18 x y - 24 y ^ { 2 }$

Solve. -The area of a circle is 144π square meters. Find its radius.

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $6 x ^ { 3 } - 60 x ^ { 2 } + 126 x$

Factor the four-term polynomial by grouping. - $8 x ^ { 4 } - 20 x ^ { 2 } + 10 x ^ { 2 } - 25$

Factor the sum or difference of two cubes. - $t ^ { 3 } + 8$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $- x ^ { 2 } - 8 x + 48$

Factor out the GCF from the polynomial. - $64 x ^ { 8 } y ^ { 9 } + 16 x ^ { 2 } y ^ { 4 } - 72 x ^ { 5 } y ^ { 2 }$

Solve. -The side of a square equals the length of a rectangle. The width of the rectangle is 4 meters longer than its length. The sum of the areas of the square and the rectangle is 198 square centimeters. Find the side of the square.

Factor the sum or difference of two cubes. - $512 p ^ { 3 + 1 }$

Find the GCF for the list. -12, 24, 27

Factor completely. - $10 x ^ { 2 } + 11 x y - 6 y ^ { 2 }$

Factor out the GCF from the polynomial. - $10 m ^ { 9 } + 4 m ^ { 6 } + 4 m ^ { 3 }$

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

Factor the trinomial by grouping. - $8 x ^ { 2 } - x - 34$

Factor completely. - $75 x ^ { 3 } - 110 x ^ { 2 } + 40 x$

Solve the equation. - $( x + 8 ) ( x + 1 ) = 44$

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 trinomial by grouping. - 3x2+11x−203 x ^ { 2 } + 11 x - 203x2+11x−20

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - 6x2−18xy−24y26 x ^ { 2 } - 18 x y - 24 y ^ { 2 }6x2−18xy−24y2