Question 1

Solve the equation.
-$( x - 2 ) ( x + 4 ) = 0$

Accepted Answer

A)  $2 , - 4$ 
B)  $2 , - 2,4 , - 4$ 
C)  $- 2,4$ 
D)  2,4 
A)  $2 , - 4$ 
B)  $2 , - 2,4 , - 4$ 
C)  $- 2,4$ 
D)  2,4

Question 2

Find a positive value of the given variable so that the trinomial is factorable.
-$5 x ^ { 2 } + 8 x + c ; c =$ ?

Accepted Answer

A)  3 
B)  9 
C)  8 
D)  4 
A)  3 
B)  9 
C)  8 
D)  4

Question 3

Match the equation with its graph.
-$y = 3 x ^ { 2 } - 3$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 4

Find the GCF for the list.
-$64 a ^ { 9 } b ^ { 3 } c ^ { 7 } , 88 a ^ { 6 } b ^ { 9 }$

Accepted Answer

A)  $4 a ^ { 6 } b ^ { 3 }$ 
B)  $8 a ^ { 6 } b ^ { 3 }$ 
C)  $8 a ^ { 6 } b ^ { 3 } c ^ { 7 }$ 
D)  $8 a ^ { 9 } b ^ { 9 }$ 
A)  $4 a ^ { 6 } b ^ { 3 }$ 
B)  $8 a ^ { 6 } b ^ { 3 }$ 
C)  $8 a ^ { 6 } b ^ { 3 } c ^ { 7 }$ 
D)  $8 a ^ { 9 } b ^ { 9 }$

Question 5

Factor the perfect square trinomial completely.
-$x ^ { 4 } + 10 x ^ { 2 } + 25$

Accepted Answer

A)  $\left( x ^ { 2 } - 5 \right) ^ { 2 }$ 
B)  $\left( x ^ { 2 } + 5 \right) \left( x ^ { 2 } - 5 \right)$ 
C)  $\left( x ^ { 2 } + 10 \right) \left( x ^ { 2 } - 10 \right)$ 
D)  $\left( x ^ { 2 } + 5 \right) ^ { 2 }$ 
A)  $\left( x ^ { 2 } - 5 \right) ^ { 2 }$ 
B)  $\left( x ^ { 2 } + 5 \right) \left( x ^ { 2 } - 5 \right)$ 
C)  $\left( x ^ { 2 } + 10 \right) \left( x ^ { 2 } - 10 \right)$ 
D)  $\left( x ^ { 2 } + 5 \right) ^ { 2 }$

Question 6

Factor the sum or difference of two cubes.
-$a ^ { 3 } b ^ { 3 } + 64$

Accepted Answer

A)  $( a b + 4 ) \left( a ^ { 2 } b ^ { 2 } - 16 \right)$ 
B)  $( a b - 4 ) \left( a ^ { 2 } b ^ { 2 } + 16 \right)$ 
C)  $( a b - 4 ) \left( a ^ { 2 } b ^ { 2 } + 4 a b + 16 \right)$ 
D)  $( a b + 4 ) \left( a ^ { 2 } b ^ { 2 } - 4 a b + 16 \right)$ 
A)  $( a b + 4 ) \left( a ^ { 2 } b ^ { 2 } - 16 \right)$ 
B)  $( a b - 4 ) \left( a ^ { 2 } b ^ { 2 } + 16 \right)$ 
C)  $( a b - 4 ) \left( a ^ { 2 } b ^ { 2 } + 4 a b + 16 \right)$ 
D)  $( a b + 4 ) \left( a ^ { 2 } b ^ { 2 } - 4 a b + 16 \right)$

Question 7

Write the perimeter of the rectangle as a simplified polynomial. Then factor this polynomial completely.
-

Accepted Answer

A)  $2 ( x - 3 ) ( x + 9 )$ 
B)  $( 2 x + 2 ) ( x + 4 )$ 
C)  $2 ( x + 2 ) ( x + 4 )$ 
D)  $( x + 2 ) ( x + 4 )$ 
A)  $2 ( x - 3 ) ( x + 9 )$ 
B)  $( 2 x + 2 ) ( x + 4 )$ 
C)  $2 ( x + 2 ) ( x + 4 )$ 
D)  $( x + 2 ) ( x + 4 )$

Question 8

Factor the trinomial by grouping.
-$14 x ^ { 3 } - 133 x ^ { 2 } + 245 x$

Accepted Answer

A)  $7 x ( x + 7 ) ( 2 x + 5 )$ 
B)  prime 
C)  $x ( 7 x - 7 ) ( 2 x - 5 )$ 
D)  $7 x ( x - 7 ) ( 2 x - 5 )$ 
A)  $7 x ( x + 7 ) ( 2 x + 5 )$ 
B)  prime 
C)  $x ( 7 x - 7 ) ( 2 x - 5 )$ 
D)  $7 x ( x - 7 ) ( 2 x - 5 )$

Question 9

Factor a negative number or a GCF with a negative coefficient from the polynomial.
-$- 6 x - 30$

Accepted Answer

A)  $6 ( - x - 5 )$ 
B)  $- 6 ( x - 5 )$ 
C)  $- 6 ( x + 5 )$ 
D)  $- 6 ( - x + 5 )$ 
A)  $6 ( - x - 5 )$ 
B)  $- 6 ( x - 5 )$ 
C)  $- 6 ( x + 5 )$ 
D)  $- 6 ( - x + 5 )$

Question 10

Factor the four-term polynomial by grouping.
-$15 x ^ { 2 } + 18 x y + 10 x y + 12 y ^ { 2 }$

Accepted Answer

A)  $( 15 x + 2 y ) ( x + 6 y )$ 
B)  $( 3 x - 2 y ) ( 5 x + 6 y )$ 
C)  $( 3 x + 2 ) ( 5 x + 6 )$ 
D)  $( 3 x + 2 y ) ( 5 x + 6 y )$ 
A)  $( 15 x + 2 y ) ( x + 6 y )$ 
B)  $( 3 x - 2 y ) ( 5 x + 6 y )$ 
C)  $( 3 x + 2 ) ( 5 x + 6 )$ 
D)  $( 3 x + 2 y ) ( 5 x + 6 y )$

Question 11

Factor out the GCF from the polynomial.
-$w ( z - 7 ) - 15 ( z - 7 )$

Accepted Answer

A)  $( z - 7 ) ( w - 15 )$ 
B)  $( w z - 7 w ) - ( 15 z - 105 )$ 
C)  $- 15 w ( z - 7 )$ 
D)  $( \mathrm { z } - 7 ) ( \mathrm { w } + 15 )$ 
A)  $( z - 7 ) ( w - 15 )$ 
B)  $( w z - 7 w ) - ( 15 z - 105 )$ 
C)  $- 15 w ( z - 7 )$ 
D)  $( \mathrm { z } - 7 ) ( \mathrm { w } + 15 )$

Question 12

Factor completely.
-$4 x ^ { 2 } - 14 x - 8$

Accepted Answer

A)  $2 ( 2 x + 1 ) ( x - 4 )$ 
B)  $2 ( 2 x - 1 ) ( x + 4 )$ 
C)  prime 
D)  $( 4 x - 2 ) ( x + 4 )$ 
A)  $2 ( 2 x + 1 ) ( x - 4 )$ 
B)  $2 ( 2 x - 1 ) ( x + 4 )$ 
C)  prime 
D)  $( 4 x - 2 ) ( x + 4 )$

Question 13

Solve the equation.
-$x ^ { 2 } - 13 x + 36 = 0$

Accepted Answer

A)  36,0 
B)  $- 4,9$ 
C)  $- 4 , - 9$ 
D)  4,9 
A)  36,0 
B)  $- 4,9$ 
C)  $- 4 , - 9$ 
D)  4,9

Question 14

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

Accepted Answer

A)  $( x + 4 ) ( x - 2 )$ 
B)  $( x - 4 ) ( x + 1 )$ 
C)  prime 
D)  $( x - 4 ) ( x + 2 )$ 
A)  $( x + 4 ) ( x - 2 )$ 
B)  $( x - 4 ) ( x + 1 )$ 
C)  prime 
D)  $( x - 4 ) ( x + 2 )$

Question 15

Find the x-intercepts of the graph of each equation.
-$y = ( 6 x - 3 ) ( x + 1 )$

Accepted Answer

A)  $\left( \frac { 1 } { 2 } , 0 \right) , ( - 1,0 )$ 
B)  $( 2,0 ) , ( 1,0 )$ 
C)  $( 2,0 ) , ( - 1,0 )$ 
D)  $( 2,0 ) , ( 0,0 )$ 
A)  $\left( \frac { 1 } { 2 } , 0 \right) , ( - 1,0 )$ 
B)  $( 2,0 ) , ( 1,0 )$ 
C)  $( 2,0 ) , ( - 1,0 )$ 
D)  $( 2,0 ) , ( 0,0 )$

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. $$\begin{array} { l l l l } 
\text { factoring } & \text { quadratic equation } & \text { perfect square trinomial } & 0 \
\text { greatest common factor } & \text { hypotenuse } & \text { sum of two cubes } & 1 \
\text { difference of two cubes } & \text { difference of two squares } & \text { triangle } & \text { leg }
\end{array}$$
-The expression $a ^ { 3 } - b ^ { 3 }$ is called $a$________

Accepted Answer

A)  sum of two cubes 
B)  difference of two squares 
C)  difference of two cubes 
D)  perfect square trinomial 
A)  sum of two cubes 
B)  difference of two squares 
C)  difference of two cubes 
D)  perfect square trinomial

Question 17

Factor the perfect square trinomial completely.
-$48 x ^ { 2 } - 168 x y + 147 y ^ { 2 }$

Accepted Answer

A)  $3 ( 4 x - 7 y ) ( 4 x + 7 y )$ 
B)  $3 ( 4 x + 7 y ) ^ { 2 }$ 
C)  $3 ( 4 x - 7 y ) ^ { 2 }$ 
D)  prime 
A)  $3 ( 4 x - 7 y ) ( 4 x + 7 y )$ 
B)  $3 ( 4 x + 7 y ) ^ { 2 }$ 
C)  $3 ( 4 x - 7 y ) ^ { 2 }$ 
D)  prime

Question 18

Solve the equation.
-$5 x ( 5 x - 8 ) ( 4 x + 3 ) = 0$

Accepted Answer

A)  $0 , \frac { 8 } { 5 } , - \frac { 3 } { 4 }$ 
B)  $0 , \frac { 3 } { 8 } , - \frac { 4 } { 3 }$ 
C)  $0 , - \frac { 8 } { 5 } , \frac { 3 } { 4 }$ 
D)  $\frac { 8 } { 5 } , - \frac { 3 } { 4 }$ 
A)  $0 , \frac { 8 } { 5 } , - \frac { 3 } { 4 }$ 
B)  $0 , \frac { 3 } { 8 } , - \frac { 4 } { 3 }$ 
C)  $0 , - \frac { 8 } { 5 } , \frac { 3 } { 4 }$ 
D)  $\frac { 8 } { 5 } , - \frac { 3 } { 4 }$

Question 19

Factor the sum or difference of two cubes.
-$343 y ^ { 3 } + 729$

Accepted Answer

A)  $( 7 y + 9 ) \left( 49 y ^ { 2 } - 63 y + 81 \right)$ 
B)  $( 7 y - 9 ) \left( 49 y ^ { 2 } + 63 y + 81 \right)$ 
C)  $( 7 y + 9 ) \left( 49 y ^ { 2 } + 63 y + 81 \right)$ 
D)  $( 343 y - 9 ) \left( y ^ { 2 } + 63 y + 81 \right)$ 
A)  $( 7 y + 9 ) \left( 49 y ^ { 2 } - 63 y + 81 \right)$ 
B)  $( 7 y - 9 ) \left( 49 y ^ { 2 } + 63 y + 81 \right)$ 
C)  $( 7 y + 9 ) \left( 49 y ^ { 2 } + 63 y + 81 \right)$ 
D)  $( 343 y - 9 ) \left( y ^ { 2 } + 63 y + 81 \right)$

Question 20

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$\mathrm { x } ^ { 2 } ( \mathrm { y } - 2 ) - 9 \mathrm { x } ( \mathrm { y } - 2 ) + 20 ( \mathrm { y } - 2 )$

Accepted Answer

A)  $( x - 4 ) ( x + 5 ) ( y - 2 )$ 
B)  $( x + 4 ) ( x + 5 ) ( y - 2 )$ 
C)  $( x + 4 ) ( x - 5 ) ( y - 2 )$ 
D)  $( x - 4 ) ( x - 5 ) ( y - 2 )$ 
A)  $( x - 4 ) ( x + 5 ) ( y - 2 )$ 
B)  $( x + 4 ) ( x + 5 ) ( y - 2 )$ 
C)  $( x + 4 ) ( x - 5 ) ( y - 2 )$ 
D)  $( x - 4 ) ( x - 5 ) ( y - 2 )$

Solve the equation. - $( x - 2 ) ( x + 4 ) = 0$

Find a positive value of the given variable so that the trinomial is factorable. - $5 x ^ { 2 } + 8 x + c ; c =$ ?

Match the equation with its graph. - $y = 3 x ^ { 2 } - 3$

Find the GCF for the list. - $64 a ^ { 9 } b ^ { 3 } c ^ { 7 } , 88 a ^ { 6 } b ^ { 9 }$

Factor the perfect square trinomial completely. - $x ^ { 4 } + 10 x ^ { 2 } + 25$

Factor the sum or difference of two cubes. - $a ^ { 3 } b ^ { 3 } + 64$

Write the perimeter of the rectangle as a simplified polynomial. Then factor this polynomial completely. -

Factor the trinomial by grouping. - $14 x ^ { 3 } - 133 x ^ { 2 } + 245 x$

Factor a negative number or a GCF with a negative coefficient from the polynomial. - $- 6 x - 30$

Factor the four-term polynomial by grouping. - $15 x ^ { 2 } + 18 x y + 10 x y + 12 y ^ { 2 }$

Factor out the GCF from the polynomial. - $w ( z - 7 ) - 15 ( z - 7 )$

Factor completely. - $4 x ^ { 2 } - 14 x - 8$

Solve the equation. - $x ^ { 2 } - 13 x + 36 = 0$

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

Find the x-intercepts of the graph of each equation. - $y = ( 6 x - 3 ) ( x + 1 )$

Factor the perfect square trinomial completely. - $48 x ^ { 2 } - 168 x y + 147 y ^ { 2 }$

Solve the equation. - $5 x ( 5 x - 8 ) ( 4 x + 3 ) = 0$

Factor the sum or difference of two cubes. - $343 y ^ { 3 } + 729$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $\mathrm { x } ^ { 2 } ( \mathrm { y } - 2 ) - 9 \mathrm { x } ( \mathrm { y } - 2 ) + 20 ( \mathrm { y } - 2 )$

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

Solve the equation. - (x−2)(x+4)=0( x - 2 ) ( x + 4 ) = 0(x−2)(x+4)=0

Find a positive value of the given variable so that the trinomial is factorable. - 5x2+8x+c;c=5 x ^ { 2 } + 8 x + c ; c =5x2+8x+c;c= ?

Match the equation with its graph. - y=3x2−3y = 3 x ^ { 2 } - 3y=3x2−3

Find the GCF for the list. - 64a9b3c7,88a6b964 a ^ { 9 } b ^ { 3 } c ^ { 7 } , 88 a ^ { 6 } b ^ { 9 }64a9b3c7,88a6b9

Factor the perfect square trinomial completely. - x4+10x2+25x ^ { 4 } + 10 x ^ { 2 } + 25x4+10x2+25

Factor the sum or difference of two cubes. - a3b3+64a ^ { 3 } b ^ { 3 } + 64a3b3+64