Question 1

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

Accepted Answer

A) True 
 B)False

Question 2

Factor the four-term polynomial by grouping.
- 6x2−9x−4x+66 x ^ { 2 } - 9 x - 4 x + 66x2−9x−4x+6

Accepted Answer

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

Question 3

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)

Question 4

Factor the four-term polynomial by grouping.
- 8a3+20a2b−10a2−25b38 a ^ { 3 } + 20 a ^ { 2 } b - 10 a ^ { 2 } - 25 b ^ { 3 }8a3+20a2b−10a2−25b3

Accepted Answer

A)    (4a2−5b2) (2a+5b) \left( 4 a ^ { 2 } - 5 b ^ { 2 } \right)  ( 2 a + 5 b ) (4a2−5b2) (2a+5b)  
B)    (4a2+5b2) (2a−5b) \left( 4 a ^ { 2 } + 5 b ^ { 2 } \right)  ( 2 a - 5 b ) (4a2+5b2) (2a−5b)  
C)    (8a2−5b2) (a+5b) \left( 8 a ^ { 2 } - 5 b ^ { 2 } \right)  ( a + 5 b ) (8a2−5b2) (a+5b)  
D)    (4a2−5b) (2a+5b) \left( 4 a ^ { 2 } - 5 b \right)  ( 2 a + 5 b ) (4a2−5b) (2a+5b)

Question 5

Factor the trinomial completely.
- 5x2+x−1205 x ^ { 2 } + x - 1205x2+x−120

Accepted Answer

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

Question 6

Find the GCF for the list.
- x2,x6x ^ { 2 } , x ^ { 6 }x2,x6

Accepted Answer

A)    x12x ^ { 12 }x12 
B)    x8x ^ { 8 }x8 
C)    x4x ^ { 4 }x4 
D)    x2x ^ { 2 }x2

Question 7

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

Question 8

Factor the trinomial completely.
- x3+16x2+64xx ^ { 3 } + 16 x ^ { 2 } + 64 xx3+16x2+64x

Accepted Answer

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

Question 9

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

Question 10

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
- z2−10z+25z ^ { 2 } - 10 z + 25z2−10z+25

Accepted Answer

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

Question 11

Factor the polynomial by grouping.
- 8a3+10a2b−12ab2−15b38 a ^ { 3 } + 10 a ^ { 2 } b - 12 a b ^ { 2 } - 15 b ^ { 3 }8a3+10a2b−12ab2−15b3

Accepted Answer

A)    (8a2−3b2) (a+5b) \left( 8 a ^ { 2 } - 3 b ^ { 2 } \right)  ( a + 5 b ) (8a2−3b2) (a+5b)  
B)    (2a2−3b) (4a+5b) \left( 2 a ^ { 2 } - 3 b \right)  ( 4 a + 5 b ) (2a2−3b) (4a+5b)  
C)    (2a2+3b2) (4a−5b) \left( 2 a ^ { 2 } + 3 b ^ { 2 } \right)  ( 4 a - 5 b ) (2a2+3b2) (4a−5b)  
D)    (2a2−3b2) (4a+5b) \left( 2 a ^ { 2 } - 3 b ^ { 2 } \right)  ( 4 a + 5 b ) (2a2−3b2) (4a+5b)

Question 12

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

Question 13

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

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

Factor the trinomial completely.
- 36x3y+96x2y+64xy36 x ^ { 3 } y + 96 x ^ { 2 } y + 64 x y36x3y+96x2y+64xy

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)

Question 16

Complete the factored form.
- 6x2−17x+12=(2x−3) 6 x ^ { 2 } - 17 x + 12 = ( 2 x - 3 ) 6x2−17x+12=(2x−3)

Accepted Answer

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

Question 17

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

Accepted Answer

A) True 
 B)False

Question 18

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
- x2+4x−45x ^ { 2 } + 4 x - 45x2+4x−45

Accepted Answer

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

Question 19

Solve the equation.
- 16t3−4t=016 t ^ { 3 } - 4 t = 016t3−4t=0

Accepted Answer

A)    12\frac { 1 } { 2 }21​ 
B)  -  −12,12- \frac { 1 } { 2 } , \frac { 1 } { 2 }−21​,21​ 
C)  0
D)  -  −12,12,0- \frac { 1 } { 2 } , \frac { 1 } { 2 } , 0−21​,21​,0

Question 20

Factor out the GCF from the polynomial.
- 5x6y+35x45 x ^ { 6 } y + 35 x ^ { 4 }5x6y+35x4

Accepted Answer

A)    5x5(xy+7x) 5 x ^ { 5 } ( x y + 7 x ) 5x5(xy+7x)  
B)    x4(5x2y+35) x ^ { 4 } \left( 5 x ^ { 2 } y + 35 \right) x4(5x2y+35)  
C)    5x4y(x2+7) 5 x ^ { 4 } y \left( x ^ { 2 } + 7 \right) 5x4y(x2+7)  
D)    5x4(x2y+7) 5 x ^ { 4 } \left( x ^ { 2 } y + 7 \right) 5x4(x2y+7)

Exam 13: Factoring Polynomials

Factor the four-term polynomial by grouping. - 6x2−9x−4x+66 x ^ { 2 } - 9 x - 4 x + 66x2−9x−4x+6

Correct AnswerverifiedShow Answer

Determine whether the trinomial is a perfect square trinomial. - b2−48b+144b ^ { 2 } - 48 b + 144b2−48b+144

Correct AnswerverifiedShow Answer

Factor the trinomial completely. - 5x2+x−1205 x ^ { 2 } + x - 1205x2+x−120

Correct AnswerverifiedShow Answer

Factor the four-term polynomial by grouping. - 8a3+20a2b−10a2−25b38 a ^ { 3 } + 20 a ^ { 2 } b - 10 a ^ { 2 } - 25 b ^ { 3 }8a3+20a2b−10a2−25b3

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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.

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

Factor the polynomial by grouping. - 8a3+10a2b−12ab2−15b38 a ^ { 3 } + 10 a ^ { 2 } b - 12 a b ^ { 2 } - 15 b ^ { 3 }8a3+10a2b−12ab2−15b3

Correct AnswerverifiedShow Answer

Factor the trinomial completely. - 36x3y+96x2y+64xy36 x ^ { 3 } y + 96 x ^ { 2 } y + 64 x y36x3y+96x2y+64xy

Correct AnswerverifiedShow Answer

Find the GCF for the list. - x2,x6x ^ { 2 } , x ^ { 6 }x2,x6

Correct AnswerverifiedShow Answer

Determine whether the trinomial is a perfect square trinomial. - 4x2−5x+64 x ^ { 2 } - 5 x + 64x2−5x+6

Correct AnswerverifiedShow Answer

Factor out the GCF from the polynomial. - 5x6y+35x45 x ^ { 6 } y + 35 x ^ { 4 }5x6y+35x4

Correct AnswerverifiedShow Answer

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - x2+4x−45x ^ { 2 } + 4 x - 45x2+4x−45

Correct AnswerverifiedShow Answer

Solve the equation. - 16t3−4t=016 t ^ { 3 } - 4 t = 016t3−4t=0

Correct AnswerverifiedShow Answer

Complete the factored form. - 6x2−17x+12=(2x−3) 6 x ^ { 2 } - 17 x + 12 = ( 2 x - 3 ) 6x2−17x+12=(2x−3)

Correct AnswerverifiedShow Answer

Factor the trinomial completely. - x3+16x2+64xx ^ { 3 } + 16 x ^ { 2 } + 64 xx3+16x2+64x

Correct AnswerverifiedShow Answer

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - z2−10z+25z ^ { 2 } - 10 z + 25z2−10z+25

Correct AnswerverifiedShow Answer

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 _____ .

Correct AnswerverifiedShow Answer

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_____ .

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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