Question 1

Fill in the blank with one of the words or phrases listed below.
 
-The_____  of a list of terms is the product of all common factors.

Accepted Answer

A) quadratic equation 
B) perfect square trinomial 
C) factoring 
D) greatest common factor 
A) quadratic equation 
B) perfect square trinomial 
C) factoring 
D) greatest common factor

Question 2

Factor out the GCF from the polynomial.
-6x + 24

Accepted Answer

A) 6(x + 24) 
B) 6(x + 4) 
C) 144x 
D) 6x + 4 
A) 6(x + 24) 
B) 6(x + 4) 
C) 144x 
D) 6x + 4

Question 3

Determine whether the trinomial is a perfect square trinomial.
-$b ^ { 2 } - 48 b + 144$

Accepted Answer

A) True 
 B)False

Question 4

Complete the factored form.
-$6 x ^ { 2 } - 17 x + 12 = ( 2 x - 3 )$

Accepted Answer

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

Question 5

Factor the polynomial by grouping.
-$8 a ^ { 3 } + 10 a ^ { 2 } b - 12 a b ^ { 2 } - 15 b ^ { 3 }$

Accepted Answer

A)  $\left( 8 a ^ { 2 } - 3 b ^ { 2 } \right) ( a + 5 b )$ 
B)  $\left( 2 a ^ { 2 } - 3 b \right) ( 4 a + 5 b )$ 
C)  $\left( 2 a ^ { 2 } + 3 b ^ { 2 } \right) ( 4 a - 5 b )$ 
D)  $\left( 2 a ^ { 2 } - 3 b ^ { 2 } \right) ( 4 a + 5 b )$ 
A)  $\left( 8 a ^ { 2 } - 3 b ^ { 2 } \right) ( a + 5 b )$ 
B)  $\left( 2 a ^ { 2 } - 3 b \right) ( 4 a + 5 b )$ 
C)  $\left( 2 a ^ { 2 } + 3 b ^ { 2 } \right) ( 4 a - 5 b )$ 
D)  $\left( 2 a ^ { 2 } - 3 b ^ { 2 } \right) ( 4 a + 5 b )$

Question 6

Factor the four-term polynomial by grouping.
-$8 a ^ { 3 } + 20 a ^ { 2 } b - 10 a ^ { 2 } - 25 b ^ { 3 }$

Accepted Answer

A)  $\left( 4 a ^ { 2 } - 5 b ^ { 2 } \right) ( 2 a + 5 b )$ 
B)  $\left( 4 a ^ { 2 } + 5 b ^ { 2 } \right) ( 2 a - 5 b )$ 
C)  $\left( 8 a ^ { 2 } - 5 b ^ { 2 } \right) ( a + 5 b )$ 
D)  $\left( 4 a ^ { 2 } - 5 b \right) ( 2 a + 5 b )$ 
A)  $\left( 4 a ^ { 2 } - 5 b ^ { 2 } \right) ( 2 a + 5 b )$ 
B)  $\left( 4 a ^ { 2 } + 5 b ^ { 2 } \right) ( 2 a - 5 b )$ 
C)  $\left( 8 a ^ { 2 } - 5 b ^ { 2 } \right) ( a + 5 b )$ 
D)  $\left( 4 a ^ { 2 } - 5 b \right) ( 2 a + 5 b )$

Question 7

Factor the trinomial completely.
-$36 x ^ { 3 } y + 96 x ^ { 2 } y + 64 x y$

Accepted Answer

A) 4xy(3x + 4)(3x + 4) 
B) 4xy(16x + 4)(x + 4) 
C) 4xy(3x + 1)(3x + 16) 
D) 4y(3x + 1)(3x + 16) 
A) 4xy(3x + 4)(3x + 4) 
B) 4xy(16x + 4)(x + 4) 
C) 4xy(3x + 1)(3x + 16) 
D) 4y(3x + 1)(3x + 16)

Question 8

Factor the trinomial completely.
-$5 x ^ { 2 } + x - 120$

Accepted Answer

A) (5x + 24)(x - 5) 
B) (5x + 5)(x - 24) 
C) (5x - 5)(x + 24) 
D) (5x - 24)(x + 5) 
A) (5x + 24)(x - 5) 
B) (5x + 5)(x - 24) 
C) (5x - 5)(x + 24) 
D) (5x - 24)(x + 5)

Question 9

Find the GCF for the list.
-$x ^ { 2 } , x ^ { 6 }$

Accepted Answer

A)  $x ^ { 12 }$ 
B)  $x ^ { 8 }$ 
C)  $x ^ { 4 }$ 
D)  $x ^ { 2 }$ 
A)  $x ^ { 12 }$ 
B)  $x ^ { 8 }$ 
C)  $x ^ { 4 }$ 
D)  $x ^ { 2 }$

Question 10

Fill in the blank with one of the words or phrases listed below.
 
-In a right triangle, each side adjacent tot he right angle is called a_____  .

Accepted Answer

A) hypotenuse 
B) quadratic equation 
C) greatest common factor 
D) leg 
A) hypotenuse 
B) quadratic equation 
C) greatest common factor 
D) leg

Question 11

Find the GCF for the list.
-15, 21, 24

Accepted Answer

A) 1 
B) 15 
C) 3 
D) 6 
A) 1 
B) 15 
C) 3 
D) 6

Question 12

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$z ^ { 2 } - 10 z + 25$

Accepted Answer

A)  $( z - 5 ) ^ { 2 }$ 
B) (z - 5)(z + 5) 
C) (z - 10)(z + 10) 
D)  $( z + 5 ) ^ { 2 }$ 
A)  $( z - 5 ) ^ { 2 }$ 
B) (z - 5)(z + 5) 
C) (z - 10)(z + 10) 
D)  $( z + 5 ) ^ { 2 }$

Question 13

Factor out the GCF from the polynomial.
-x(y + 2)+ 9(y +2)

Accepted Answer

A) 2y(x + 9) 
B) 9x(y +2) 
C) (y +2)(x + 9) 
D) (xy + 2x)+ (9y + 18) 
A) 2y(x + 9) 
B) 9x(y +2) 
C) (y +2)(x + 9) 
D) (xy + 2x)+ (9y + 18)

Question 14

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$x ^ { 2 } + 4 x - 45$

Accepted Answer

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

Question 15

Factor the trinomial completely.
-$x ^ { 3 } + 16 x ^ { 2 } + 64 x$

Accepted Answer

A) x(x + 8)(x - 8) 
B)  $\mathrm { x } ( \mathrm { x } + 8 ) ^ { 2 }$ 
C)  $x ( x - 8 ) ^ { 2 }$ 
D) prime 
A) x(x + 8)(x - 8) 
B)  $\mathrm { x } ( \mathrm { x } + 8 ) ^ { 2 }$ 
C)  $x ( x - 8 ) ^ { 2 }$ 
D) prime

Question 16

Determine whether the trinomial is a perfect square trinomial.
-$4 x ^ { 2 } - 5 x + 6$

Accepted Answer

A) True 
 B)False

Question 17

Factor out the GCF from the polynomial.
-$5 x ^ { 6 } y + 35 x ^ { 4 }$

Accepted Answer

A)  $5 x ^ { 5 } ( x y + 7 x )$ 
B)  $x ^ { 4 } \left( 5 x ^ { 2 } y + 35 \right)$ 
C)  $5 x ^ { 4 } y \left( x ^ { 2 } + 7 \right)$ 
D)  $5 x ^ { 4 } \left( x ^ { 2 } y + 7 \right)$ 
A)  $5 x ^ { 5 } ( x y + 7 x )$ 
B)  $x ^ { 4 } \left( 5 x ^ { 2 } y + 35 \right)$ 
C)  $5 x ^ { 4 } y \left( x ^ { 2 } + 7 \right)$ 
D)  $5 x ^ { 4 } \left( x ^ { 2 } y + 7 \right)$

Question 18

Fill in the blank with one of the words or phrases listed below.
 
-A trinomial that is the square of some binomial is called a _____ .

Accepted Answer

A) perfect square trinomial 
B) factoring 
C) greatest common factor 
D) quadratic equation 
A) perfect square trinomial 
B) factoring 
C) greatest common factor 
D) quadratic equation

Question 19

Solve the equation.
-$16 t ^ { 3 } - 4 t = 0$

Accepted Answer

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

Question 20

Factor the four-term polynomial by grouping.
-$6 x ^ { 2 } - 9 x - 4 x + 6$

Accepted Answer

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

Fill in the blank with one of the words or phrases listed below. -The_____ of a list of terms is the product of all common factors.

Factor out the GCF from the polynomial. -6x + 24

Determine whether the trinomial is a perfect square trinomial. - $b ^ { 2 } - 48 b + 144$

Complete the factored form. - $6 x ^ { 2 } - 17 x + 12 = ( 2 x - 3 )$

Factor the polynomial by grouping. - $8 a ^ { 3 } + 10 a ^ { 2 } b - 12 a b ^ { 2 } - 15 b ^ { 3 }$

Factor the four-term polynomial by grouping. - $8 a ^ { 3 } + 20 a ^ { 2 } b - 10 a ^ { 2 } - 25 b ^ { 3 }$

Factor the trinomial completely. - $36 x ^ { 3 } y + 96 x ^ { 2 } y + 64 x y$

Factor the trinomial completely. - $5 x ^ { 2 } + x - 120$

Find the GCF for the list. - $x ^ { 2 } , x ^ { 6 }$

Fill in the blank with one of the words or phrases listed below. -In a right triangle, each side adjacent tot he right angle is called a_____ .

Find the GCF for the list. -15, 21, 24

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $z ^ { 2 } - 10 z + 25$

Factor out the GCF from the polynomial. -x(y + 2)+ 9(y +2)

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $x ^ { 2 } + 4 x - 45$

Factor the trinomial completely. - $x ^ { 3 } + 16 x ^ { 2 } + 64 x$

Determine whether the trinomial is a perfect square trinomial. - $4 x ^ { 2 } - 5 x + 6$

Factor out the GCF from the polynomial. - $5 x ^ { 6 } y + 35 x ^ { 4 }$

Fill in the blank with one of the words or phrases listed below. -A trinomial that is the square of some binomial is called a _____ .

Solve the equation. - $16 t ^ { 3 } - 4 t = 0$

Factor the four-term polynomial by grouping. - $6 x ^ { 2 } - 9 x - 4 x + 6$

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Exam 13: Factoring Polynomials