Question 1

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime.
-$6 z ^ { 2 } - 5 z - 6$

Accepted Answer

A)  $( 3 z + 2 ) ( 2 z - 3 )$ 
B)  $( 6 z + 2 ) ( z - 3 )$ 
C)  $( 3 z - 2 ) ( 2 z + 3 )$ 
D)  prime 
A)  $( 3 z + 2 ) ( 2 z - 3 )$ 
B)  $( 6 z + 2 ) ( z - 3 )$ 
C)  $( 3 z - 2 ) ( 2 z + 3 )$ 
D)  prime

Question 2

Factor out the GCF from the polynomial.
-$64 x ^ { 8 } y ^ { 9 } - 40 x ^ { 2 } y ^ { 7 } + 64 x ^ { 6 } y ^ { 3 }$

Accepted Answer

A)  $x ^ { 2 } y ^ { 3 } \left( 64 x ^ { 6 } y ^ { 6 } - 40 y ^ { 4 } + 64 x ^ { 4 } \right)$ 
B)  $8 x ^ { 2 } \left( 8 x ^ { 6 } y ^ { 9 } - 5 y ^ { 7 } + 8 x ^ { 4 } y ^ { 3 } \right)$ 
C)  $8 \left( 8 x ^ { 8 } y ^ { 9 } - 5 x ^ { 2 } y ^ { 7 } + 8 x ^ { 6 } y ^ { 3 } \right)$ 
D)  $8 x ^ { 2 } y ^ { 3 } \left( 8 x ^ { 6 } y ^ { 6 } - 5 y ^ { 4 } + 8 x ^ { 4 } \right)$ 
A)  $x ^ { 2 } y ^ { 3 } \left( 64 x ^ { 6 } y ^ { 6 } - 40 y ^ { 4 } + 64 x ^ { 4 } \right)$ 
B)  $8 x ^ { 2 } \left( 8 x ^ { 6 } y ^ { 9 } - 5 y ^ { 7 } + 8 x ^ { 4 } y ^ { 3 } \right)$ 
C)  $8 \left( 8 x ^ { 8 } y ^ { 9 } - 5 x ^ { 2 } y ^ { 7 } + 8 x ^ { 6 } y ^ { 3 } \right)$ 
D)  $8 x ^ { 2 } y ^ { 3 } \left( 8 x ^ { 6 } y ^ { 6 } - 5 y ^ { 4 } + 8 x ^ { 4 } \right)$

Question 3

Factor completely.
-$$x ^ { 2 } + 5 x - 14$$

Accepted Answer

A)  $( x - 7 ) ( x + 1 )$ 
B)  prime 
C)  $( x - 7 ) ( x + 2 )$ 
D)  $( x + 7 ) ( x - 2 )$ 
A)  $( x - 7 ) ( x + 1 )$ 
B)  prime 
C)  $( x - 7 ) ( x + 2 )$ 
D)  $( x + 7 ) ( x - 2 )$

Question 4

Factor completely.
-x2+ 12xy + 27y2

Accepted Answer

A)  (x - 9y)(x + y) 
B)  (x + 9y)(x + 3y) 
C)  (x - 9y)(x + 3y) 
D)  prime 
A)  (x - 9y)(x + y) 
B)  (x + 9y)(x + 3y) 
C)  (x - 9y)(x + 3y) 
D)  prime

Question 5

Factor the polynomial using the greatest common binomial factor.
-$x ( x + 3 ) + 6 ( x + 3 )$

Accepted Answer

A)  $\left( x ^ { 2 } + 3 x \right) ( 6 x + 18 )$ 
B)  $( x - 3 ) ( x - 6 )$ 
C)  $( x + 3 ) ( x + 6 )$ 
D)  $\left( x ^ { 2 } + 3 \right) \left( x ^ { 2 } + 6 \right)$ 
A)  $\left( x ^ { 2 } + 3 x \right) ( 6 x + 18 )$ 
B)  $( x - 3 ) ( x - 6 )$ 
C)  $( x + 3 ) ( x + 6 )$ 
D)  $\left( x ^ { 2 } + 3 \right) \left( x ^ { 2 } + 6 \right)$

Question 6

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is
prime.
-$9 x ^ { 2 } + 18 x + 8$

Accepted Answer

A)  $( 9 x + 2 ) ( x + 4 )$ 
B)  prime 
C)  $( 3 x + 2 ) ( 3 x + 4 )$ 
D)  $( 3 x - 2 ) ( 3 x - 4 )$ 
A)  $( 9 x + 2 ) ( x + 4 )$ 
B)  prime 
C)  $( 3 x + 2 ) ( 3 x + 4 )$ 
D)  $( 3 x - 2 ) ( 3 x - 4 )$

Question 7

Factor the polynomial using the greatest common binomial factor.
-$8 x ^ { 2 } ( 8 x - 5 ) + 8 x - 5$

Accepted Answer

A)  $9 x ^ { 2 } ( 8 x - 5 )$ 
B)  $2 ( 8 x - 5 ) \left( 8 x ^ { 2 } \right)$ 
C)  $9 x ^ { 2 } \left( 8 x ^ { 2 } + 1 \right)$ 
D)  $( 8 x - 5 ) \left( 8 x ^ { 2 } + 1 \right)$ 
A)  $9 x ^ { 2 } ( 8 x - 5 )$ 
B)  $2 ( 8 x - 5 ) \left( 8 x ^ { 2 } \right)$ 
C)  $9 x ^ { 2 } \left( 8 x ^ { 2 } + 1 \right)$ 
D)  $( 8 x - 5 ) \left( 8 x ^ { 2 } + 1 \right)$

Question 8

Factor by grouping.
-$10 x ^ { 10 } - 15 x ^ { 5 } y ^ { 4 } + 6 x ^ { 5 } y ^ { 4 } - 9 y ^ { 8 }$

Accepted Answer

A)  $\left( 5 x ^ { 5 } + 3 y \right) \left( 2 x ^ { 5 } - 3 y ^ { 8 } \right)$ 
B)  $\left( 5 x ^ { 5 } + 3 y ^ { 4 } \right) \left( 2 x ^ { 5 } - 3 y ^ { 4 } \right)$ 
C)  $\left( 10 x ^ { 5 } + 3 y ^ { 4 } \right) \left( x ^ { 5 } - 3 y ^ { 4 } \right)$ 
D)  $\left( 5 x ^ { 5 } - 3 y ^ { 4 } \right) \left( 2 x ^ { 5 } + 3 y ^ { 4 } \right)$ 
A)  $\left( 5 x ^ { 5 } + 3 y \right) \left( 2 x ^ { 5 } - 3 y ^ { 8 } \right)$ 
B)  $\left( 5 x ^ { 5 } + 3 y ^ { 4 } \right) \left( 2 x ^ { 5 } - 3 y ^ { 4 } \right)$ 
C)  $\left( 10 x ^ { 5 } + 3 y ^ { 4 } \right) \left( x ^ { 5 } - 3 y ^ { 4 } \right)$ 
D)  $\left( 5 x ^ { 5 } - 3 y ^ { 4 } \right) \left( 2 x ^ { 5 } + 3 y ^ { 4 } \right)$

Question 9

Find the greatest common factor of the monomials.
-10xy, 10x2, 12xy2, and 6y2

Accepted Answer

A)  4 
B)  2x 
C)  2 
D)  2xy 
A)  4 
B)  2x 
C)  2 
D)  2xy

Question 10

Factor completely. If unfactorable, indicate that the polynomial is prime.
-$$\mathrm { s } ^ { 8 } - \mathrm { t } ^ { 18 }$$

Accepted Answer

A)  $\left( s ^ { 6 } + t ^ { 16 } \right) \left( s ^ { 6 } - t ^ { 16 } \right)$ 
B)  $\left( s ^ { 4 } - t ^ { 9 } \right) ^ { 2 }$ 
C)  $\left( s ^ { 4 } + t ^ { 9 } \right) \left( s ^ { 4 } - t ^ { 9 } \right)$ 
D)  $\left( s ^ { 6 } - t ^ { 16 } \right) ^ { 2 }$ 
A)  $\left( s ^ { 6 } + t ^ { 16 } \right) \left( s ^ { 6 } - t ^ { 16 } \right)$ 
B)  $\left( s ^ { 4 } - t ^ { 9 } \right) ^ { 2 }$ 
C)  $\left( s ^ { 4 } + t ^ { 9 } \right) \left( s ^ { 4 } - t ^ { 9 } \right)$ 
D)  $\left( s ^ { 6 } - t ^ { 16 } \right) ^ { 2 }$

Question 11

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is
prime.
-$16 x ^ { 2 } + 16 x t + 3 t ^ { 2 }$

Accepted Answer

A)  $( 4 x + t ) ( 4 x + 3 t )$ 
B)  prime 
C)  $( 4 x - t ) ( 4 x - 3 t )$ 
D)  $( 16 x + t ) ( x + 3 t )$ 
A)  $( 4 x + t ) ( 4 x + 3 t )$ 
B)  prime 
C)  $( 4 x - t ) ( 4 x - 3 t )$ 
D)  $( 16 x + t ) ( x + 3 t )$

Question 12

Factor the polynomial using the negative of the greatest common factor.
-$$- 27 x ^ { 3 } y ^ { 2 } + 6 x ^ { 3 } y - 12 x ^ { 2 } y$$

Accepted Answer

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

Question 13

Factor by grouping.
-$x ^ { 2 } - 4 x - 3 x + 12$

Accepted Answer

A)  $( x - 3 ) ( x + 8 )$ 
B)  $( x + 3 ) ( x - 4 )$ 
C)  $- 7 x \left( x ^ { 2 } + 12 \right)$ 
D)  $( x - 3 ) ( x - 4 )$ 
A)  $( x - 3 ) ( x + 8 )$ 
B)  $( x + 3 ) ( x - 4 )$ 
C)  $- 7 x \left( x ^ { 2 } + 12 \right)$ 
D)  $( x - 3 ) ( x - 4 )$

Question 14

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is
prime.
-$$25 x ^ { 3 } y ^ { 4 } + 30 x ^ { 2 } y ^ { 5 } + 8 x y ^ { 6 }$$

Accepted Answer

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

Question 15

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is
prime.
-96x2 + 56xy + 8y2

Accepted Answer

A)  prime 
B)  (24x + 8y)(4x + y) 
C)  8(3x - y)(4x - y) 
D)  8(3x + y)(4x + y) 
A)  prime 
B)  (24x + 8y)(4x + y) 
C)  8(3x - y)(4x - y) 
D)  8(3x + y)(4x + y)

Question 16

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime.
-$20 x ^ { 2 } y ^ { 2 } - 7 x y ^ { 2 } - 6 y ^ { 2 }$

Accepted Answer

A)  $( 5 x + 2 y ) ( 4 x - 3 y )$ 
B)  $y ^ { 2 } ( 5 x + 2 ) ( 4 x - 3 )$ 
C)  $y ^ { 2 } ( x + 2 ) ( 20 x - 3 )$ 
D)  $( 4 x + 2 y ) ( 5 x - 3 y )$ 
A)  $( 5 x + 2 y ) ( 4 x - 3 y )$ 
B)  $y ^ { 2 } ( 5 x + 2 ) ( 4 x - 3 )$ 
C)  $y ^ { 2 } ( x + 2 ) ( 20 x - 3 )$ 
D)  $( 4 x + 2 y ) ( 5 x - 3 y )$

Question 17

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime.
-$$20 x ^ { 2 } + 27 x + 9$$

Accepted Answer

A)  $( 4 x - 3 ) ( 5 x - 3 )$ 
B)  prime 
C)  $( 4 x + 3 ) ( 5 x + 3 )$ 
D)  $( 20 x + 3 ) ( x + 3 )$ 
A)  $( 4 x - 3 ) ( 5 x - 3 )$ 
B)  prime 
C)  $( 4 x + 3 ) ( 5 x + 3 )$ 
D)  $( 20 x + 3 ) ( x + 3 )$

Question 18

Factor completely.
-x2 - 10x + 24

Accepted Answer

A)  prime 
B)  (x - 6)(x - 4) 
C)  (x + 6)(x - 4) 
D)  (x + 6)(x + 1) 
A)  prime 
B)  (x - 6)(x - 4) 
C)  (x + 6)(x - 4) 
D)  (x + 6)(x + 1)

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - $6 z ^ { 2 } - 5 z - 6$

Factor out the GCF from the polynomial. - $64 x ^ { 8 } y ^ { 9 } - 40 x ^ { 2 } y ^ { 7 } + 64 x ^ { 6 } y ^ { 3 }$

Factor completely. - $x ^ { 2 } + 5 x - 14$

Factor completely. -x²+ 12xy + 27y²

Factor the polynomial using the greatest common binomial factor. - $x ( x + 3 ) + 6 ( x + 3 )$

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - $9 x ^ { 2 } + 18 x + 8$

Factor the polynomial using the greatest common binomial factor. - $8 x ^ { 2 } ( 8 x - 5 ) + 8 x - 5$

Factor by grouping. - $10 x ^ { 10 } - 15 x ^ { 5 } y ^ { 4 } + 6 x ^ { 5 } y ^ { 4 } - 9 y ^ { 8 }$

Find the greatest common factor of the monomials. -10xy, 10x², 12xy², and 6y²

Factor completely. If unfactorable, indicate that the polynomial is prime. - $\mathrm { s } ^ { 8 } - \mathrm { t } ^ { 18 }$

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - $16 x ^ { 2 } + 16 x t + 3 t ^ { 2 }$

Factor the polynomial using the negative of the greatest common factor. - $- 27 x ^ { 3 } y ^ { 2 } + 6 x ^ { 3 } y - 12 x ^ { 2 } y$

Factor by grouping. - $x ^ { 2 } - 4 x - 3 x + 12$

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - $25 x ^ { 3 } y ^ { 4 } + 30 x ^ { 2 } y ^ { 5 } + 8 x y ^ { 6 }$

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is prime. -96x² + 56xy + 8y²

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - $20 x ^ { 2 } y ^ { 2 } - 7 x y ^ { 2 } - 6 y ^ { 2 }$

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - $20 x ^ { 2 } + 27 x + 9$

Factor completely. -x² - 10x + 24

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Exam 6: Factoring Polynomials

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - 6z2−5z−66 z ^ { 2 } - 5 z - 66z2−5z−6

Factor out the GCF from the polynomial. - 64x8y9−40x2y7+64x6y364 x ^ { 8 } y ^ { 9 } - 40 x ^ { 2 } y ^ { 7 } + 64 x ^ { 6 } y ^ { 3 }64x8y9−40x2y7+64x6y3

Factor completely. - x2+5x−14x ^ { 2 } + 5 x - 14x2+5x−14

Factor completely. -x2+ 12xy + 27y2

Factor the polynomial using the greatest common binomial factor. - x(x+3)+6(x+3)x ( x + 3 ) + 6 ( x + 3 )x(x+3)+6(x+3)

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - 9x2+18x+89 x ^ { 2 } + 18 x + 89x2+18x+8

Factor the polynomial using the greatest common binomial factor. - 8x2(8x−5)+8x−58 x ^ { 2 } ( 8 x - 5 ) + 8 x - 58x2(8x−5)+8x−5

Factor by grouping. - 10x10−15x5y4+6x5y4−9y810 x ^ { 10 } - 15 x ^ { 5 } y ^ { 4 } + 6 x ^ { 5 } y ^ { 4 } - 9 y ^ { 8 }10x10−15x5y4+6x5y4−9y8

Find the greatest common factor of the monomials. -10xy, 10x2, 12xy2, and 6y2

Factor completely. If unfactorable, indicate that the polynomial is prime. - s8−t18\mathrm { s } ^ { 8 } - \mathrm { t } ^ { 18 }s8−t18

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - 16x2+16xt+3t216 x ^ { 2 } + 16 x t + 3 t ^ { 2 }16x2+16xt+3t2

Factor the polynomial using the negative of the greatest common factor. - −27x3y2+6x3y−12x2y- 27 x ^ { 3 } y ^ { 2 } + 6 x ^ { 3 } y - 12 x ^ { 2 } y−27x3y2+6x3y−12x2y

Factor by grouping. - x2−4x−3x+12x ^ { 2 } - 4 x - 3 x + 12x2−4x−3x+12

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - 25x3y4+30x2y5+8xy625 x ^ { 3 } y ^ { 4 } + 30 x ^ { 2 } y ^ { 5 } + 8 x y ^ { 6 }25x3y4+30x2y5+8xy6

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is prime. -96x2 + 56xy + 8y2

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - 20x2y2−7xy2−6y220 x ^ { 2 } y ^ { 2 } - 7 x y ^ { 2 } - 6 y ^ { 2 }20x2y2−7xy2−6y2

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - 20x2+27x+920 x ^ { 2 } + 27 x + 920x2+27x+9

Factor completely. -x2 - 10x + 24