Question 1

Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$6 x ^ { 3 } - 48$

Accepted Answer

A)  $6 ( x - 2 ) \left( x ^ { 2 } + 2 x + 4 \right)$ 
B)  $6 ( x - 12 ) \left( x ^ { 2 } + 12 x + 24 \right)$ 
C)  $6 ( x - 2 ) \left( x ^ { 2 } - 2 x + 4 \right)$ 
D)  $6 ( x + 2 ) \left( x ^ { 2 } - 2 x + 4 \right)$ 
A)  $6 ( x - 2 ) \left( x ^ { 2 } + 2 x + 4 \right)$ 
B)  $6 ( x - 12 ) \left( x ^ { 2 } + 12 x + 24 \right)$ 
C)  $6 ( x - 2 ) \left( x ^ { 2 } - 2 x + 4 \right)$ 
D)  $6 ( x + 2 ) \left( x ^ { 2 } - 2 x + 4 \right)$

Question 2

Solve the equation.
-$10 x ^ { 3 } + 70 x ^ { 2 } + 120 x = 0$

Accepted Answer

A)  $0,4,3$ 
B)  $0 , - 4 , - 3$ 
C)  $- \frac { 1 } { 4 } , - 3$ 
D)  $- 4 , - 3$ 
A)  $0,4,3$ 
B)  $0 , - 4 , - 3$ 
C)  $- \frac { 1 } { 4 } , - 3$ 
D)  $- 4 , - 3$

Question 3

Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$x ^ { 2 } - x - 54$

Accepted Answer

A)  $( x - 6 ) ( x + 9 )$ 
B)  $( x - 54 ) ( x + 1 )$ 
C)  $( x + 6 ) ( x - 9 )$ 
D)  prime 
A)  $( x - 6 ) ( x + 9 )$ 
B)  $( x - 54 ) ( x + 1 )$ 
C)  $( x + 6 ) ( x - 9 )$ 
D)  prime

Question 4

Solve the equation.
-$( 3 x + 1 ) ( 5 x - 2 ) = 0$

Accepted Answer

A)  2,3 
B)  $3 , \frac { 5 } { 2 }$ 
C)  $\frac { 1 } { 3 } , - \frac { 2 } { 5 }$ 
D)  $- \frac { 1 } { 3 } , \frac { 2 } { 5 }$ 
A)  2,3 
B)  $3 , \frac { 5 } { 2 }$ 
C)  $\frac { 1 } { 3 } , - \frac { 2 } { 5 }$ 
D)  $- \frac { 1 } { 3 } , \frac { 2 } { 5 }$

Question 5

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$\mathrm { u } ^ { 2 } - 4 u \mathrm { v } - 32 \mathrm { v } ^ { 2 }$

Accepted Answer

A)  $( u - 4 v ) ( u + v )$ 
B)  prime 
C)  $( \mathrm { u } + 4 \mathrm { v } ) ( \mathrm { u } - 8 \mathrm { v } )$ 
D)  $( u - 4 v ) ( u + 8 v )$ 
A)  $( u - 4 v ) ( u + v )$ 
B)  prime 
C)  $( \mathrm { u } + 4 \mathrm { v } ) ( \mathrm { u } - 8 \mathrm { v } )$ 
D)  $( u - 4 v ) ( u + 8 v )$

Question 6

Solve the equation.
-$2 x ^ { 2 } - 5 x - 7 = 0$

Accepted Answer

A)  $\frac { 2 } { 7 } , - 1$ 
B)  $\frac { 2 } { 7 } , 1$ 
C)  $\frac { 2 } { 7 } , 0$ 
D)  $\frac { 7 } { 2 } , - 1$ 
A)  $\frac { 2 } { 7 } , - 1$ 
B)  $\frac { 2 } { 7 } , 1$ 
C)  $\frac { 2 } { 7 } , 0$ 
D)  $\frac { 7 } { 2 } , - 1$

Question 7

Factor the four-term polynomial by grouping.
-$12 a ^ { 3 } + 18 a ^ { 2 } b - 10 a b ^ { 2 } - 15 b ^ { 3 }$

Accepted Answer

A)  $\left( 12 a ^ { 2 } - 5 b ^ { 2 } \right) ( a + 3 b )$ 
B)  $\left( 6 a ^ { 2 } + 5 b ^ { 2 } \right) ( 2 a - 3 b )$ 
C)  $\left( 6 a ^ { 2 } - 5 b \right) ( 2 a + 3 b )$ 
D)  $\left( 6 a ^ { 2 } - 5 b ^ { 2 } \right) ( 2 a + 3 b )$ 
A)  $\left( 12 a ^ { 2 } - 5 b ^ { 2 } \right) ( a + 3 b )$ 
B)  $\left( 6 a ^ { 2 } + 5 b ^ { 2 } \right) ( 2 a - 3 b )$ 
C)  $\left( 6 a ^ { 2 } - 5 b \right) ( 2 a + 3 b )$ 
D)  $\left( 6 a ^ { 2 } - 5 b ^ { 2 } \right) ( 2 a + 3 b )$

Question 8

Factor out the GCF from the polynomial.
-$4 ( y + 7 ) - x ( y + 7 )$

Accepted Answer

A)  $( y - 7 ) ( x - 4 )$ 
B)  $( 4 y + 28 ) - ( x y + 7 x )$ 
C)  $( \mathrm { y } + 7 ) ( 4 - \mathrm { x } )$ 
D)  $( y + 7 ) ( 4 + x )$ 
A)  $( y - 7 ) ( x - 4 )$ 
B)  $( 4 y + 28 ) - ( x y + 7 x )$ 
C)  $( \mathrm { y } + 7 ) ( 4 - \mathrm { x } )$ 
D)  $( y + 7 ) ( 4 + x )$

Question 9

Find the GCF for the list.
-\)x ^ { 4 } , x ^ { 6 }\(

Accepted Answer

A)  $x ^ { 2 }$ 
B)  $x ^ { 4 }$ 
C)  $x ^ { 24 }$ 
D)  $x ^ { 10 }$ 
A)  $x ^ { 2 }$ 
B)  $x ^ { 4 }$ 
C)  $x ^ { 24 }$ 
D)  $x ^ { 10 }$

Question 10

Factor the trinomial by grouping.
-$14 x ^ { 3 } + 29 x ^ { 2 } + 12 x$

Accepted Answer

A)  prime 
B)  $x ( 2 x + 4 ) ( 7 x + 3 )$ 
C)  $2 x ( x + 3 ) ( 7 x + 4 )$ 
D)  $x ( 2 x + 3 ) ( 7 x + 4 )$ 
A)  prime 
B)  $x ( 2 x + 4 ) ( 7 x + 3 )$ 
C)  $2 x ( x + 3 ) ( 7 x + 4 )$ 
D)  $x ( 2 x + 3 ) ( 7 x + 4 )$

Question 11

Find the GCF for the list.
-$64 a ^ { 8 } b ^ { 3 } , 88 a ^ { 5 } b ^ { 8 }$

Accepted Answer

A)  $4 a ^ { 3 } b ^ { 5 }$ 
B)  $8 a ^ { 5 } b ^ { 3 }$ 
C)  $704 a ^ { 8 } b ^ { 8 }$ 
D)  $8 a ^ { 8 } b ^ { 8 }$ 
A)  $4 a ^ { 3 } b ^ { 5 }$ 
B)  $8 a ^ { 5 } b ^ { 3 }$ 
C)  $704 a ^ { 8 } b ^ { 8 }$ 
D)  $8 a ^ { 8 } b ^ { 8 }$

Question 12

Factor the trinomial by grouping.
-$15 y ^ { 2 } - 19 y + 6$

Accepted Answer

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

Question 13

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

Question 14

Find the GCF for the list.
-$23 \mathrm {~b} ^ { 2 } , 23 \mathrm {~b} ^ { 2 } \mathrm { k } ^ { 2 } , 11 \mathrm {~b} ^ { 6 }$

Accepted Answer

A)  $b ^ { 2 } \mathrm { k } ^ { 2 }$ 
B)  $23 b ^ { 2 } k ^ { 2 }$ 
C)  $b ^ { 2 }$ 
D)  $23 b ^ { 2 }$ 
A)  $b ^ { 2 } \mathrm { k } ^ { 2 }$ 
B)  $23 b ^ { 2 } k ^ { 2 }$ 
C)  $b ^ { 2 }$ 
D)  $23 b ^ { 2 }$

Question 15

Factor out the GCF from the polynomial.
-$x ( y + 7 ) + 5 ( y + 7 )$

Accepted Answer

A)  $( x y + 7 x ) + ( 5 y + 35 )$ 
B)  $7 y ( x + 5 )$ 
C)  $( \mathrm { y } + 7 ) ( \mathrm { x } + 5 )$ 
D)  $5 x ( y + 7 )$ 
A)  $( x y + 7 x ) + ( 5 y + 35 )$ 
B)  $7 y ( x + 5 )$ 
C)  $( \mathrm { y } + 7 ) ( \mathrm { x } + 5 )$ 
D)  $5 x ( y + 7 )$

Question 16

Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$25 - \mathrm { m } ^ { 2 }$

Accepted Answer

A)  prime 
B)  $( 5 - \mathrm { m } ) ^ { 2 }$ 
C)  $( 5 - \mathrm { m } ) ( 5 + \mathrm { m } )$ 
D)  $( 5 + \mathrm { m } ) ^ { 2 }$ 
A)  prime 
B)  $( 5 - \mathrm { m } ) ^ { 2 }$ 
C)  $( 5 - \mathrm { m } ) ( 5 + \mathrm { m } )$ 
D)  $( 5 + \mathrm { m } ) ^ { 2 }$

Question 17

Factor the four-term polynomial by grouping.
-$12 x ^ { 2 } - 16 x + 15 x - 20$

Accepted Answer

A)  $( 4 x + 5 ) ( 3 x - 4 )$ 
B)  $( 4 x - 5 ) ( 3 x + 4 )$ 
C)  $( 12 x - 5 ) ( x + 4 )$ 
D)  $( 12 x + 5 ) ( x - 4 )$ 
A)  $( 4 x + 5 ) ( 3 x - 4 )$ 
B)  $( 4 x - 5 ) ( 3 x + 4 )$ 
C)  $( 12 x - 5 ) ( x + 4 )$ 
D)  $( 12 x + 5 ) ( x - 4 )$

Question 18

Factor completely.
-$12 x ^ { 4 } - 17 x ^ { 3 } + 6 x ^ { 2 }$

Accepted Answer

A)  $\left( 12 x ^ { 2 } + 3 \right) \left( x ^ { 2 } + 2 \right)$ 
B)  $x ( 4 x + 3 ) ( 3 x + 2 )$ 
C)  $x ^ { 2 } ( 12 x - 1 ) ( x - 6 )$ 
D)  $x ^ { 2 } ( 4 x - 3 ) ( 3 x - 2 )$ 
A)  $\left( 12 x ^ { 2 } + 3 \right) \left( x ^ { 2 } + 2 \right)$ 
B)  $x ( 4 x + 3 ) ( 3 x + 2 )$ 
C)  $x ^ { 2 } ( 12 x - 1 ) ( x - 6 )$ 
D)  $x ^ { 2 } ( 4 x - 3 ) ( 3 x - 2 )$

Question 19

Solve.
-The area of a square is 36 square miles. Find the length of a side of the square.

Accepted Answer

A)  18 mi 
B)  -6 mi 
C)  6 mi 
D)  9 mi 
A)  18 mi 
B)  -6 mi 
C)  6 mi 
D)  9 mi

Question 20

Solve the equation.
-$17 x ^ { 2 } - 6 x = 0$

Accepted Answer

A)  $\frac { 17 } { 6 } , 0$ 
B)  $- \frac { 6 } { 17 } , 0$ 
C)  $\frac { 6 } { 17 } , 0$ 
D)  $- \frac { 17 } { 6 } , 0$ 
A)  $\frac { 17 } { 6 } , 0$ 
B)  $- \frac { 6 } { 17 } , 0$ 
C)  $\frac { 6 } { 17 } , 0$ 
D)  $- \frac { 17 } { 6 } , 0$

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $6 x ^ { 3 } - 48$

Solve the equation. - $10 x ^ { 3 } + 70 x ^ { 2 } + 120 x = 0$

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $x ^ { 2 } - x - 54$

Solve the equation. - $( 3 x + 1 ) ( 5 x - 2 ) = 0$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $\mathrm { u } ^ { 2 } - 4 u \mathrm { v } - 32 \mathrm { v } ^ { 2 }$

Solve the equation. - $2 x ^ { 2 } - 5 x - 7 = 0$

Factor the four-term polynomial by grouping. - $12 a ^ { 3 } + 18 a ^ { 2 } b - 10 a b ^ { 2 } - 15 b ^ { 3 }$

Factor out the GCF from the polynomial. - $4 ( y + 7 ) - x ( y + 7 )$

Find the GCF for the list. -\)x ^ { 4 } , x ^ { 6 } \(

Factor the trinomial by grouping. - $14 x ^ { 3 } + 29 x ^ { 2 } + 12 x$

Find the GCF for the list. - $64 a ^ { 8 } b ^ { 3 } , 88 a ^ { 5 } b ^ { 8 }$

Factor the trinomial by grouping. - $15 y ^ { 2 } - 19 y + 6$

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.

Find the GCF for the list. - $23 \mathrm {~b} ^ { 2 } , 23 \mathrm {~b} ^ { 2 } \mathrm { k } ^ { 2 } , 11 \mathrm {~b} ^ { 6 }$

Factor out the GCF from the polynomial. - $x ( y + 7 ) + 5 ( y + 7 )$

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $25 - \mathrm { m } ^ { 2 }$

Factor the four-term polynomial by grouping. - $12 x ^ { 2 } - 16 x + 15 x - 20$

Factor completely. - $12 x ^ { 4 } - 17 x ^ { 3 } + 6 x ^ { 2 }$

Solve. -The area of a square is 36 square miles. Find the length of a side of the square.

Solve the equation. - $17 x ^ { 2 } - 6 x = 0$

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 polynomial completely. If the polynomial cannot be factored, write "prime." - 6x3−486 x ^ { 3 } - 486x3−48

Solve the equation. - 10x3+70x2+120x=010 x ^ { 3 } + 70 x ^ { 2 } + 120 x = 010x3+70x2+120x=0

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - x2−x−54x ^ { 2 } - x - 54x2−x−54

Solve the equation. - (3x+1)(5x−2)=0( 3 x + 1 ) ( 5 x - 2 ) = 0(3x+1)(5x−2)=0

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - u2−4uv−32v2\mathrm { u } ^ { 2 } - 4 u \mathrm { v } - 32 \mathrm { v } ^ { 2 }u2−4uv−32v2

Solve the equation. - 2x2−5x−7=02 x ^ { 2 } - 5 x - 7 = 02x2−5x−7=0

Factor the four-term polynomial by grouping. - 12a3+18a2b−10ab2−15b312 a ^ { 3 } + 18 a ^ { 2 } b - 10 a b ^ { 2 } - 15 b ^ { 3 }12a3+18a2b−10ab2−15b3

Factor out the GCF from the polynomial. - 4(y+7)−x(y+7)4 ( y + 7 ) - x ( y + 7 )4(y+7)−x(y+7)