Question 1

Factor out the GCF from the polynomial.
-$6 m ^ { 9 } + 16 m ^ { 6 } + 4 m ^ { 3 }$

Accepted Answer

A)  $2 \left( 3 m ^ { 9 } + 8 m ^ { 6 } + 2 m ^ { 3 } \right)$ 
B) No common factor 
C)  $m ^ { 3 } \left( 6 m ^ { 6 } + 16 m ^ { 3 } + 4 \right)$ 
D)  $2 m ^ { 3 } \left( 3 m ^ { 6 } + 8 m ^ { 3 } + 2 \right)$ 
A)  $2 \left( 3 m ^ { 9 } + 8 m ^ { 6 } + 2 m ^ { 3 } \right)$ 
B) No common factor 
C)  $m ^ { 3 } \left( 6 m ^ { 6 } + 16 m ^ { 3 } + 4 \right)$ 
D)  $2 m ^ { 3 } \left( 3 m ^ { 6 } + 8 m ^ { 3 } + 2 \right)$ D

Question 2

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$2 x ^ { 2 } - 20 x + 42$

Accepted Answer

A) 2(x + 7)(x + 3) 
B) 2(x - 7)(x - 3) 
C) (x + 7)(2x + 6) 
D) (2x + 7)(x + 3) 
A) 2(x + 7)(x + 3) 
B) 2(x - 7)(x - 3) 
C) (x + 7)(2x + 6) 
D) (2x + 7)(x + 3) B

Question 3

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

Accepted Answer

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

Question 4

Factor out the GCF from the polynomial.
-40x - 20

Accepted Answer

A) 20(2x) 
B) 20(2x - 1) 
C) 5(8x - 4) 
D) 4(10x - 5) 
A) 20(2x) 
B) 20(2x - 1) 
C) 5(8x - 4) 
D) 4(10x - 5)

Question 5

Solve the equation.
-x(3x + 4)= 4

Accepted Answer

A)  $0 , \frac { 4 } { 3 }$ 
B)  $0 , - \frac { 4 } { 3 }$ 
C)  $\frac { 2 } { 3 } , - 2$ 
D)  $\frac { 3 } { 2 } , 2$ 
A)  $0 , \frac { 4 } { 3 }$ 
B)  $0 , - \frac { 4 } { 3 }$ 
C)  $\frac { 2 } { 3 } , - 2$ 
D)  $\frac { 3 } { 2 } , 2$

Question 6

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$4 x ^ { 2 } + 12 x - 40$

Accepted Answer

A) (x - 2)(4x + 20) 
B) (4x + 8)(x - 5) 
C) 4(x + 2)(x - 5) 
D) 4(x - 2)(x + 5) 
A) (x - 2)(4x + 20) 
B) (4x + 8)(x - 5) 
C) 4(x + 2)(x - 5) 
D) 4(x - 2)(x + 5)

Question 7

Determine whether the trinomial is a perfect square trinomial.
-$x ^ { 2 } + 22 x + 121$

Accepted Answer

A) True 
 B)False

Question 8

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$x ^ { 2 } + 50 x + 625$

Accepted Answer

A) (x + 25)(x - 25) 
B)  $( x - 25 ) ^ { 2 }$ 
C)  $( x + 25 ) ^ { 2 }$ 
D) prime 
A) (x + 25)(x - 25) 
B)  $( x - 25 ) ^ { 2 }$ 
C)  $( x + 25 ) ^ { 2 }$ 
D) prime

Question 9

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

Accepted Answer

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

Question 10

Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$9 - m ^ { 2 }$

Accepted Answer

A)  $( 3 + \mathrm { m } ) ^ { 2 }$ 
B)  $( 3 - m ) ^ { 2 }$ 
C) (3 - m)(3 + m) 
D) Prime 
A)  $( 3 + \mathrm { m } ) ^ { 2 }$ 
B)  $( 3 - m ) ^ { 2 }$ 
C) (3 - m)(3 + m) 
D) Prime

Question 11

Factor the binomial completely.
-$9 x ^ { 2 } - 16$

Accepted Answer

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

Question 12

Factor the four-term polynomial by grouping.
-xy + y + 6x + 6

Accepted Answer

A) (x + 1)(y + 6) 
B) (x + 6)(y + 1) 
C) (x + 1)(6y + 6) 
D) (6x + 6)(y + 1) 
A) (x + 1)(y + 6) 
B) (x + 6)(y + 1) 
C) (x + 1)(6y + 6) 
D) (6x + 6)(y + 1)

Question 13

Factor the trinomial completely.
-$p ^ { 2 } - 6 p q + 36 q ^ { 2 }$

Accepted Answer

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

Question 14

Factor the four-term polynomial by grouping.
-$20 a ^ { 3 } + 15 a ^ { 2 } b + 24 a b ^ { 2 } + 18 b ^ { 3 }$

Accepted Answer

A)  $\left( 20 a ^ { 2 } + 6 b ^ { 2 } \right) ( a + 3 b )$ 
B)  $\left( 5 a ^ { 2 } - 6 b ^ { 2 } \right) ( 4 a - 3 b )$ 
C)  $\left( 5 a ^ { 2 } + 6 b \right) ( 4 a + 3 b )$ 
D)  $\left( 5 a ^ { 2 } + 6 b ^ { 2 } \right) ( 4 a + 3 b )$ 
A)  $\left( 20 a ^ { 2 } + 6 b ^ { 2 } \right) ( a + 3 b )$ 
B)  $\left( 5 a ^ { 2 } - 6 b ^ { 2 } \right) ( 4 a - 3 b )$ 
C)  $\left( 5 a ^ { 2 } + 6 b \right) ( 4 a + 3 b )$ 
D)  $\left( 5 a ^ { 2 } + 6 b ^ { 2 } \right) ( 4 a + 3 b )$

Question 15

Factor the trinomial completely.
-$7 m ^ { 5 } + 50 m ^ { 3 } n ^ { 2 } + 7 m n ^ { 4 }$

Accepted Answer

A)  $m \left( 7 m ^ { 2 } + n ^ { 2 } \right) ^ { 2 }$ 
B)   $m \left( 7 m ^ { 2 } + n ^ { 2 } \right) \left( m ^ { 2 } + 7 n ^ { 2 } \right)$ 
C)  $m \left( 7 m ^ { 2 } + 7 n ^ { 2 } \right) ^ { 2 }$ 
D) prime 
A)  $m \left( 7 m ^ { 2 } + n ^ { 2 } \right) ^ { 2 }$ 
B)   $m \left( 7 m ^ { 2 } + n ^ { 2 } \right) \left( m ^ { 2 } + 7 n ^ { 2 } \right)$ 
C)  $m \left( 7 m ^ { 2 } + 7 n ^ { 2 } \right) ^ { 2 }$ 
D) prime

Question 16

Solve.
-The hypotenuse of a right triangle is 8 feet less than three times the shorter leg and the longer leg is 8 feet more than twice the shorter leg. Find the lengths of the three sides of the triangle.

Accepted Answer

A) 20 ft, 48 ft, 52 ft 
B) 30 ft, 68 ft, 82 ft 
C) 15 ft, 36 ft, 39 ft 
D) 18 ft, 44 ft, 46 ft 
A) 20 ft, 48 ft, 52 ft 
B) 30 ft, 68 ft, 82 ft 
C) 15 ft, 36 ft, 39 ft 
D) 18 ft, 44 ft, 46 ft

Question 17

Factor the trinomial completely.
-$- 64 x ^ { 3 } + 64 x ^ { 2 } + 20 x$

Accepted Answer

A)   $- 4 \left( 4 x ^ { 2 } + 1 \right) ( 4 x - 5 )$ 
B)  $- 4 x ( 4 x + 1 ) ( 4 x - 5 )$ 
C)  $x ( 4 x + 1 ) ( - 16 x + 20 )$ 
D)  $x ( - 16 x - 4 ) ( 4 x - 5 )$ 
A)   $- 4 \left( 4 x ^ { 2 } + 1 \right) ( 4 x - 5 )$ 
B)  $- 4 x ( 4 x + 1 ) ( 4 x - 5 )$ 
C)  $x ( 4 x + 1 ) ( - 16 x + 20 )$ 
D)  $x ( - 16 x - 4 ) ( 4 x - 5 )$

Question 18

Factor the four-term polynomial by grouping.
-$8 x ^ { 2 } - 10 x y + 12 x y - 15 y ^ { 2 }$

Accepted Answer

A) (8x + 3y)(x - 5y) 
B) (2x + 3y)(4x - 5y) 
C) (2x - 3y)(4x - 5y) 
D) (2x + 3)(4x - 5) 
A) (8x + 3y)(x - 5y) 
B) (2x + 3y)(4x - 5y) 
C) (2x - 3y)(4x - 5y) 
D) (2x + 3)(4x - 5)

Question 19

Solve.
-A window washer accidentally drops a bucket from the top of a 400-foot building. The height h of the bucket after t seconds is given byn by $h = - 16 t ^ { 2 } + 400$ When will the buck When will the bucket hit the ground?

Accepted Answer

A) 80 sec 
B) 25 sec 
C) 5 sec 
D) -5 sec 
A) 80 sec 
B) 25 sec 
C) 5 sec 
D) -5 sec

Question 20

Find the GCF for the list.
-20x, 4

Accepted Answer

A) 1 
B) 4 
C) 5x 
D) 20x 
A) 1 
B) 4 
C) 5x 
D) 20x

Factor out the GCF from the polynomial. - $6 m ^ { 9 } + 16 m ^ { 6 } + 4 m ^ { 3 }$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $2 x ^ { 2 } - 20 x + 42$

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

Factor out the GCF from the polynomial. -40x - 20

Solve the equation. -x(3x + 4)= 4

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $4 x ^ { 2 } + 12 x - 40$

Determine whether the trinomial is a perfect square trinomial. - $x ^ { 2 } + 22 x + 121$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $x ^ { 2 } + 50 x + 625$

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

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $9 - m ^ { 2 }$

Factor the binomial completely. - $9 x ^ { 2 } - 16$

Factor the four-term polynomial by grouping. -xy + y + 6x + 6

Factor the trinomial completely. - $p ^ { 2 } - 6 p q + 36 q ^ { 2 }$

Factor the four-term polynomial by grouping. - $20 a ^ { 3 } + 15 a ^ { 2 } b + 24 a b ^ { 2 } + 18 b ^ { 3 }$

Factor the trinomial completely. - $7 m ^ { 5 } + 50 m ^ { 3 } n ^ { 2 } + 7 m n ^ { 4 }$

Solve. -The hypotenuse of a right triangle is 8 feet less than three times the shorter leg and the longer leg is 8 feet more than twice the shorter leg. Find the lengths of the three sides of the triangle.

Factor the trinomial completely. - $- 64 x ^ { 3 } + 64 x ^ { 2 } + 20 x$

Factor the four-term polynomial by grouping. - $8 x ^ { 2 } - 10 x y + 12 x y - 15 y ^ { 2 }$

Solve. -A window washer accidentally drops a bucket from the top of a 400-foot building. The height h of the bucket after t seconds is given byn by $h = - 16 t ^ { 2 } + 400$ When will the buck When will the bucket hit the ground?

Find the GCF for the list. -20x, 4

The Whole Numbers

Multiplying and Dividing Fractions

Adding and Subtracting Fractions

Decimals

Ratio, Proportion, and Percent

Geometry

Statistics and Probability

Real Numbers and Introduction to Algebra

Equations, Inequalities, and Problem Solving

Graphing Equations and Inequalities

Systems of Equations

Exponents and Polynomials

Rational Expressions

Roots and Radicals

Quadratic Equations and Nonlinear Graphs

Algebraic Equations and Inequalities

Filters

Exam 13: Factoring Polynomials

Factor out the GCF from the polynomial. - 6m9+16m6+4m36 m ^ { 9 } + 16 m ^ { 6 } + 4 m ^ { 3 }6m9+16m6+4m3

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - 2x2−20x+422 x ^ { 2 } - 20 x + 422x2−20x+42

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - x2+2xy−24y2x ^ { 2 } + 2 x y - 24 y ^ { 2 }x2+2xy−24y2