Question 1

Solve the equation.
-x(5x + 30)= 0

Accepted Answer

A) 0, -6 
B)  $0 , \frac { 1 } { 6 }$ 
C) 0, 6 
D)  $0 , - \frac { 1 } { 6 }$ 
A) 0, -6 
B)  $0 , \frac { 1 } { 6 }$ 
C) 0, 6 
D)  $0 , - \frac { 1 } { 6 }$

Question 2

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

Accepted Answer

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

Question 3

Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$x ^ { 4 } - 256$

Accepted Answer

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

Question 4

Solve the equation.
-$x ^ { 2 } - x = 56$

Accepted Answer

A) 7, 8 
B) 1, 56 
C) -7, -8 
D) -7, 8 
A) 7, 8 
B) 1, 56 
C) -7, -8 
D) -7, 8

Question 5

Factor the trinomial completely.
-  $147 x ^ { 2 } + 336 x y + 192 y ^ { 2 }$

Accepted Answer

A)  $3 ( 7 x - 8 y ) ^ { 2 }$ 
B) 3(7x + 8y)(7x - 8y) 
C)  $3 ( 7 x + 8 y ) ^ { 2 }$ 
D) prime 
A)  $3 ( 7 x - 8 y ) ^ { 2 }$ 
B) 3(7x + 8y)(7x - 8y) 
C)  $3 ( 7 x + 8 y ) ^ { 2 }$ 
D) prime

Question 6

Factor out the GCF from the polynomial.
-$s \left( t ^ { 2 } - 10 \right) + 2 \left( t ^ { 2 } - 10 \right)$

Accepted Answer

A)  $\left( t ^ { 2 } - 10 \right) ( s + 2 )$ 
B)  $\left( t ^ { 2 } - 10 \right) ( s - 2 )$ 
C)  $\left( s t ^ { 2 } - 10 s \right) + \left( 2 t ^ { 2 } - 20 \right)$ 
D)  $2 \mathrm {~s} \left( \mathrm { t } ^ { 2 } - 10 \right)$ 
A)  $\left( t ^ { 2 } - 10 \right) ( s + 2 )$ 
B)  $\left( t ^ { 2 } - 10 \right) ( s - 2 )$ 
C)  $\left( s t ^ { 2 } - 10 s \right) + \left( 2 t ^ { 2 } - 20 \right)$ 
D)  $2 \mathrm {~s} \left( \mathrm { t } ^ { 2 } - 10 \right)$

Question 7

Factor the trinomial completely.
-$12 x ^ { 2 } + 7 x - 12$

Accepted Answer

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

Question 8

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$5 x ^ { 2 } - 30 x + 5 x ^ { 3 }$

Accepted Answer

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

Question 9

Factor the trinomial completely.
-$49 x ^ { 2 } - 84 x + 36$

Accepted Answer

A) (7x - 6)(7x + 6) 
B)  $( 7 x - 6 ) ^ { 2 }$ 
C)  $( 7 x + 6 ) ^ { 2 }$ 
D) (49x + 1)(x + 36) 
A) (7x - 6)(7x + 6) 
B)  $( 7 x - 6 ) ^ { 2 }$ 
C)  $( 7 x + 6 ) ^ { 2 }$ 
D) (49x + 1)(x + 36)

Question 10

Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$x ^ { 2 } + 81$

Accepted Answer

A)  $( x + 9 ) ^ { 2 }$ 
B)  $( x - 9 ) ^ { 2 }$ 
C) (x + 9)(x - 9) 
D) prime 
A)  $( x + 9 ) ^ { 2 }$ 
B)  $( x - 9 ) ^ { 2 }$ 
C) (x + 9)(x - 9) 
D) prime

Question 11

Factor the trinomial completely.
-$35 x ^ { 3 } - 190 x ^ { 2 } + 75 x$

Accepted Answer

A) 5x(x - 5)(7x - 3) 
B) x(5x - 5)(7x - 3) 
C) 5x(x + 5)(7x + 3) 
D) prime 
A) 5x(x - 5)(7x - 3) 
B) x(5x - 5)(7x - 3) 
C) 5x(x + 5)(7x + 3) 
D) prime

Question 12

Find the GCF for the list.
-$15 \mathrm {~m} ^ { 3 } \cdot 135 \mathrm {~m} ^ { 9 }$

Accepted Answer

A) 2025m6 
B) 15m6 
C)  $135 \mathrm {~m} ^ { 3 }$ 
D)  $15 \mathrm {~m} ^ { 3 }$ 
A) 2025m6 
B) 15m6 
C)  $135 \mathrm {~m} ^ { 3 }$ 
D)  $15 \mathrm {~m} ^ { 3 }$

Question 13

Factor the trinomial completely.
-$24 x ^ { 2 } + 14 x y + 2 y ^ { 2 }$

Accepted Answer

A) 2(3x - y)(4x - y) 
B) (6x + 2y)(4x + y) 
C) 2(3x + y)(4x + y) 
D) prime 
A) 2(3x - y)(4x - y) 
B) (6x + 2y)(4x + y) 
C) 2(3x + y)(4x + y) 
D) prime

Question 14

Fill in the blank with one of the words or phrases listed below.
 
-_____ is the process of writing an expression as a product.

Accepted Answer

A) Quadratic equation 
B) Factoring 
C) Perfect square trinomial 
D) Greatest common factor 
A) Quadratic equation 
B) Factoring 
C) Perfect square trinomial 
D) Greatest common factor

Question 15

Factor the trinomial completely.
-$2 x ^ { 2 } + 23 x + 11$

Accepted Answer

A) (2x - 1)(x - 11) 
B) (2x + 11)(x + 1) 
C) (2x + 1)(x + 11) 
D) prime 
A) (2x - 1)(x - 11) 
B) (2x + 11)(x + 1) 
C) (2x + 1)(x + 11) 
D) prime

Question 16

Factor out the GCF from the polynomial.
-$27 y ^ { 3 } - 6 y ^ { 2 } + 12 y$

Accepted Answer

A)  $3 \left( 9 y ^ { 3 } - 2 y ^ { 2 } + 4 y \right)$ 
B)  $y \left( 27 y ^ { 2 } - 6 y + 12 \right)$ 
C)  $3 y \left( 9 y ^ { 3 } - 2 y ^ { 2 } + 4 y \right)$ 
D)  $3 y \left( 9 y ^ { 2 } - 2 y + 4 \right)$ 
A)  $3 \left( 9 y ^ { 3 } - 2 y ^ { 2 } + 4 y \right)$ 
B)  $y \left( 27 y ^ { 2 } - 6 y + 12 \right)$ 
C)  $3 y \left( 9 y ^ { 3 } - 2 y ^ { 2 } + 4 y \right)$ 
D)  $3 y \left( 9 y ^ { 2 } - 2 y + 4 \right)$

Question 17

Solve.
-If the sides of a square are increased by 2 meters, the area becomes 81 square meters. Find the length of a side of the original square.

Accepted Answer

A) 7 m 
B) 2 m 
C) 9 m 
D) 11 m 
A) 7 m 
B) 2 m 
C) 9 m 
D) 11 m

Question 18

Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$7 x ^ { 2 } - 29 x + 24$

Accepted Answer

A) (7x - 8)(7x + 3) 
B) (7x - 8)(x - 3) 
C) 7(x - 8)(x - 3) 
D) (7x + 3)(x - 8) 
A) (7x - 8)(7x + 3) 
B) (7x - 8)(x - 3) 
C) 7(x - 8)(x - 3) 
D) (7x + 3)(x - 8)

Question 19

Factor a -1 from the polynomial.
-$8 x ^ { 6 } - 9 x ^ { 5 }$

Accepted Answer

A)  $- 1 \left( - 8 x ^ { 6 } + 9 x ^ { 5 } \right)$ 
B)  $- 1 \left( 8 x ^ { 6 } + 9 x ^ { 5 } \right)$ 
C)  $- 1 \left( - 9 x ^ { 6 } + 8 x ^ { 5 } \right)$ 
D)  $- 1 \left( - 8 x ^ { 6 } - 9 x ^ { 5 } \right)$ 
A)  $- 1 \left( - 8 x ^ { 6 } + 9 x ^ { 5 } \right)$ 
B)  $- 1 \left( 8 x ^ { 6 } + 9 x ^ { 5 } \right)$ 
C)  $- 1 \left( - 9 x ^ { 6 } + 8 x ^ { 5 } \right)$ 
D)  $- 1 \left( - 8 x ^ { 6 } - 9 x ^ { 5 } \right)$

Question 20

Solve the equation.
-b(b + 17)= 0

Accepted Answer

A) -1, -17 
B) 17, 0 
C) -17, 0 
D) 1, -17 
A) -1, -17 
B) 17, 0 
C) -17, 0 
D) 1, -17

Solve the equation. -x(5x + 30)= 0

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

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $x ^ { 4 } - 256$

Solve the equation. - $x ^ { 2 } - x = 56$

Factor the trinomial completely. - $147 x ^ { 2 } + 336 x y + 192 y ^ { 2 }$

Factor out the GCF from the polynomial. - $s \left( t ^ { 2 } - 10 \right) + 2 \left( t ^ { 2 } - 10 \right)$

Factor the trinomial completely. - $12 x ^ { 2 } + 7 x - 12$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $5 x ^ { 2 } - 30 x + 5 x ^ { 3 }$

Factor the trinomial completely. - $49 x ^ { 2 } - 84 x + 36$

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $x ^ { 2 } + 81$

Factor the trinomial completely. - $35 x ^ { 3 } - 190 x ^ { 2 } + 75 x$

Find the GCF for the list. - $15 \mathrm {~m} ^ { 3 } \cdot 135 \mathrm {~m} ^ { 9 }$

Factor the trinomial completely. - $24 x ^ { 2 } + 14 x y + 2 y ^ { 2 }$

Fill in the blank with one of the words or phrases listed below. -_____ is the process of writing an expression as a product.

Factor the trinomial completely. - $2 x ^ { 2 } + 23 x + 11$

Factor out the GCF from the polynomial. - $27 y ^ { 3 } - 6 y ^ { 2 } + 12 y$

Solve. -If the sides of a square are increased by 2 meters, the area becomes 81 square meters. Find the length of a side of the original square.

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $7 x ^ { 2 } - 29 x + 24$

Factor a -1 from the polynomial. - $8 x ^ { 6 } - 9 x ^ { 5 }$

Solve the equation. -b(b + 17)= 0

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Exam 13: Factoring Polynomials

Solve the equation. -x(5x + 30)= 0

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - 2x−48+x22 x - 48 + x ^ { 2 }2x−48+x2

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - x4−256x ^ { 4 } - 256x4−256

Solve the equation. - x2−x=56x ^ { 2 } - x = 56x2−x=56

Factor the trinomial completely. - 147x2+336xy+192y2147 x ^ { 2 } + 336 x y + 192 y ^ { 2 }147x2+336xy+192y2

Factor out the GCF from the polynomial. - s(t2−10)+2(t2−10)s \left( t ^ { 2 } - 10 \right) + 2 \left( t ^ { 2 } - 10 \right)s(t2−10)+2(t2−10)

Factor the trinomial completely. - 12x2+7x−1212 x ^ { 2 } + 7 x - 1212x2+7x−12

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - 5x2−30x+5x35 x ^ { 2 } - 30 x + 5 x ^ { 3 }5x2−30x+5x3

Factor the trinomial completely. - 49x2−84x+3649 x ^ { 2 } - 84 x + 3649x2−84x+36

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - x2+81x ^ { 2 } + 81x2+81

Factor the trinomial completely. - 35x3−190x2+75x35 x ^ { 3 } - 190 x ^ { 2 } + 75 x35x3−190x2+75x

Find the GCF for the list. - 15 m3⋅135 m915 \mathrm {~m} ^ { 3 } \cdot 135 \mathrm {~m} ^ { 9 }15 m3⋅135 m9

Factor the trinomial completely. - 24x2+14xy+2y224 x ^ { 2 } + 14 x y + 2 y ^ { 2 }24x2+14xy+2y2