Question 1

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

Accepted Answer

A)  $3 , - 5$ 
B)  3,5 
C)  $3 , - 3,5 , - 5$ 
D)  $- 3,5$ 
A)  $3 , - 5$ 
B)  3,5 
C)  $3 , - 3,5 , - 5$ 
D)  $- 3,5$

Question 2

Factor the trinomial by grouping.
-$6 z ^ { 2 } + 5 z - 6$

Accepted Answer

A)  $( 6 z + 3 ) ( z - 2 )$ 
B)  prime 
C)  $( 2 z - 3 ) ( 3 z + 2 )$ 
D)  $( 2 z + 3 ) ( 3 z - 2 )$ 
A)  $( 6 z + 3 ) ( z - 2 )$ 
B)  prime 
C)  $( 2 z - 3 ) ( 3 z + 2 )$ 
D)  $( 2 z + 3 ) ( 3 z - 2 )$

Question 3

Factor out the GCF from the polynomial.
-$p q ( p - 4 ) + ( p - 4 )$

Accepted Answer

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

Question 4

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$x ^ { 2 } + 47 x + 48$

Accepted Answer

A)  $( x + 48 ) ( x - 1 )$ 
B)  $( x + 48 ) ( x + 1 )$ 
C)  prime 
D)  $( x + 8 ) ( x + 6 )$ 
A)  $( x + 48 ) ( x - 1 )$ 
B)  $( x + 48 ) ( x + 1 )$ 
C)  prime 
D)  $( x + 8 ) ( x + 6 )$

Question 5

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$a ^ { 3 } b ^ { 2 } + 5 a ^ { 2 } b - 24 a$

Accepted Answer

A)  $a ( a b + 8 ) ( a b - 3 )$ 
B)  $a \left( a ^ { 2 } b ^ { 2 } + 5 a b - 24 \right)$ 
C)  $a ( a b - 8 ) ( a b + 3 )$ 
D)  $a ^ { 2 } ( b + 8 ) ( b - 3 )$ 
A)  $a ( a b + 8 ) ( a b - 3 )$ 
B)  $a \left( a ^ { 2 } b ^ { 2 } + 5 a b - 24 \right)$ 
C)  $a ( a b - 8 ) ( a b + 3 )$ 
D)  $a ^ { 2 } ( b + 8 ) ( b - 3 )$

Question 6

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$x ^ { 2 } - x - 45$

Accepted Answer

A)  $( x + 5 ) ( x - 9 )$ 
B)  prime 
C)  $( x - 5 ) ( x + 9 )$ 
D)  $( x - 45 ) ( x + 1 )$ 
A)  $( x + 5 ) ( x - 9 )$ 
B)  prime 
C)  $( x - 5 ) ( x + 9 )$ 
D)  $( x - 45 ) ( x + 1 )$

Question 7

Factor out the GCF from the polynomial.
-$22 x - 11$

Accepted Answer

A)  $11 \mathrm { x } ( 2 \mathrm { x } - 1 )$ 
B)  $11 x ( 2 - 1 )$ 
C)  $11 ( 2 x - 1 )$ 
D)  $11 ( x - 2 )$ 
A)  $11 \mathrm { x } ( 2 \mathrm { x } - 1 )$ 
B)  $11 x ( 2 - 1 )$ 
C)  $11 ( 2 x - 1 )$ 
D)  $11 ( x - 2 )$

Question 8

Find the GCF for the list.
-140, 60

Accepted Answer

A)  1 
B)  5 
C)  2 
D)  20 
A)  1 
B)  5 
C)  2 
D)  20

Question 9

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

Accepted Answer

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

Question 10

Factor the perfect square trinomial completely.
-$p ^ { 2 } - 8 p q + 64 q ^ { 2 }$

Accepted Answer

A)  prime 
B)  $( p + 8 q ) ( p - 8 q )$ 
C)  $( p - 8 q ) ^ { 2 }$ 
D)  $( p + 8 q ) ^ { 2 }$ 
A)  prime 
B)  $( p + 8 q ) ( p - 8 q )$ 
C)  $( p - 8 q ) ^ { 2 }$ 
D)  $( p + 8 q ) ^ { 2 }$

Question 11

Solve the equation.
-$y ^ { 3 } + 6 y ^ { 2 } + 9 y = 0$

Accepted Answer

A)  $0 , - 3$ 
B)  $0 , - 3,3$ 
C)  $3 , - 3$ 
D)  0,3 
A)  $0 , - 3$ 
B)  $0 , - 3,3$ 
C)  $3 , - 3$ 
D)  0,3

Question 12

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

Accepted Answer

A)  $8 ( x - 2 ) ( x + 3 )$ 
B)  $( 8 x + 16 ) ( x - 3 )$ 
C)  $8 ( x + 2 ) ( x - 3 )$ 
D)  prime 
A)  $8 ( x - 2 ) ( x + 3 )$ 
B)  $( 8 x + 16 ) ( x - 3 )$ 
C)  $8 ( x + 2 ) ( x - 3 )$ 
D)  prime

Question 13

Represent each given condition using a single variable, x.
-The length and width of a rectangle whose width is nine times its length.

Accepted Answer

A)  length = x; width = 9x 
B)  width = x; length = x + 9 
C)  length = x; width = x + 9 
D)  width = x; length = 9x 
A)  length = x; width = 9x 
B)  width = x; length = x + 9 
C)  length = x; width = x + 9 
D)  width = x; length = 9x

Question 14

Solve the equation.
-$( 8 y + 21 ) ( 5 y + 22 ) = 0$

Accepted Answer

A)  $- \frac { 21 } { 8 } , - \frac { 22 } { 5 }$ 
B)  $- \frac { 8 } { 13 } , - \frac { 5 } { 22 }$ 
C)  13,17 
D)  $\frac { 21 } { 8 } , \frac { 22 } { 5 }$ 
A)  $- \frac { 21 } { 8 } , - \frac { 22 } { 5 }$ 
B)  $- \frac { 8 } { 13 } , - \frac { 5 } { 22 }$ 
C)  13,17 
D)  $\frac { 21 } { 8 } , \frac { 22 } { 5 }$

Question 15

Match the equation with its graph.
-$y = x ( x - 4 )$

Accepted Answer

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

Question 16

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

Accepted Answer

A)  $( x + 1 ) ( 3 y + 3 )$ 
B)  $( x + 1 ) ( y + 3 )$ 
C)  $( 3 x + 3 ) ( y + 1 )$ 
D)  $( x + 3 ) ( y + 1 )$ 
A)  $( x + 1 ) ( 3 y + 3 )$ 
B)  $( x + 1 ) ( y + 3 )$ 
C)  $( 3 x + 3 ) ( y + 1 )$ 
D)  $( x + 3 ) ( y + 1 )$

Question 17

Solve the equation.
-$16 x ^ { 2 } = 7 x$

Accepted Answer

A)  $0 , \frac { 16 } { 7 }$ 
B)  $- \frac { 7 } { 16 } , 0$ 
C)  $0 , \frac { 7 } { 16 }$ 
D)  $- \frac { 16 } { 7 } , 0$ 
A)  $0 , \frac { 16 } { 7 }$ 
B)  $- \frac { 7 } { 16 } , 0$ 
C)  $0 , \frac { 7 } { 16 }$ 
D)  $- \frac { 16 } { 7 } , 0$

Question 18

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$48 + 47 x + x ^ { 2 }$

Accepted Answer

A)  prime 
B)  $( x + 8 ) ( x + 6 )$ 
C)  $( x + 48 ) ( x - 1 )$ 
D)  $( x + 48 ) ( x + 1 )$ 
A)  prime 
B)  $( x + 8 ) ( x + 6 )$ 
C)  $( x + 48 ) ( x - 1 )$ 
D)  $( x + 48 ) ( x + 1 )$

Question 19

Find a positive value of the given variable so that the trinomial is factorable.
-$x ^ { 2 } + b x - 7 ; b = ?$

Accepted Answer

A)  7 
B)  8 
C)  9 
D)  6 
A)  7 
B)  8 
C)  9 
D)  6

Question 20

Factor completely.
-$25 p ^ { 4 } - 30 p ^ { 3 } + 9 p ^ { 2 }$

Accepted Answer

A)  $p ^ { 2 } ( 5 p - 3 ) ( 5 p + 3 )$ 
B)  $p ^ { 2 } ( 25 p + 1 ) ( p + 9 )$ 
C)  $p ^ { 2 } ( 5 p + 3 ) ^ { 2 }$ 
D)  $p ^ { 2 } ( 5 p - 3 ) ^ { 2 }$ 
A)  $p ^ { 2 } ( 5 p - 3 ) ( 5 p + 3 )$ 
B)  $p ^ { 2 } ( 25 p + 1 ) ( p + 9 )$ 
C)  $p ^ { 2 } ( 5 p + 3 ) ^ { 2 }$ 
D)  $p ^ { 2 } ( 5 p - 3 ) ^ { 2 }$

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

Factor the trinomial by grouping. - $6 z ^ { 2 } + 5 z - 6$

Factor out the GCF from the polynomial. - $p q ( p - 4 ) + ( p - 4 )$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $x ^ { 2 } + 47 x + 48$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $a ^ { 3 } b ^ { 2 } + 5 a ^ { 2 } b - 24 a$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $x ^ { 2 } - x - 45$

Factor out the GCF from the polynomial. - $22 x - 11$

Find the GCF for the list. -140, 60

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

Factor the perfect square trinomial completely. - $p ^ { 2 } - 8 p q + 64 q ^ { 2 }$

Solve the equation. - $y ^ { 3 } + 6 y ^ { 2 } + 9 y = 0$

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

Represent each given condition using a single variable, x. -The length and width of a rectangle whose width is nine times its length.

Solve the equation. - $( 8 y + 21 ) ( 5 y + 22 ) = 0$

Match the equation with its graph. - $y = x ( x - 4 )$

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

Solve the equation. - $16 x ^ { 2 } = 7 x$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $48 + 47 x + x ^ { 2 }$

Find a positive value of the given variable so that the trinomial is factorable. - $x ^ { 2 } + b x - 7 ; b = ?$

Factor completely. - $25 p ^ { 4 } - 30 p ^ { 3 } + 9 p ^ { 2 }$

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−3)(x+5)=0( x - 3 ) ( x + 5 ) = 0(x−3)(x+5)=0

Factor the trinomial by grouping. - 6z2+5z−66 z ^ { 2 } + 5 z - 66z2+5z−6

Factor out the GCF from the polynomial. - pq(p−4)+(p−4)p q ( p - 4 ) + ( p - 4 )pq(p−4)+(p−4)

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - x2+47x+48x ^ { 2 } + 47 x + 48x2+47x+48

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - a3b2+5a2b−24aa ^ { 3 } b ^ { 2 } + 5 a ^ { 2 } b - 24 aa3b2+5a2b−24a

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - x2−x−45x ^ { 2 } - x - 45x2−x−45

Factor out the GCF from the polynomial. - 22x−1122 x - 1122x−11