Question 1

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime.
-$$12 x ^ { 2 } + 25 x t + 12 t ^ { 2 }$$

Accepted Answer

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

Question 2

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime.
-$$2 x ^ { 2 } - 7 x - 15$$

Accepted Answer

A)  prime 
B)  $( 2 x + 3 ) ( x - 5 )$ 
C)  $( 2 x - 5 ) ( x + 3 )$ 
D)  $( 2 x - 3 ) ( x + 5 )$ 
A)  prime 
B)  $( 2 x + 3 ) ( x - 5 )$ 
C)  $( 2 x - 5 ) ( x + 3 )$ 
D)  $( 2 x - 3 ) ( x + 5 )$ B

Question 3

Factor completely. If unfactorable, indicate that the polynomial is prime.
-$$\mathrm { z } ^ { 2 } - 49$$

Accepted Answer

A)  $( z + 7 ) ( z - 7 )$ 
B)  $( z - 7 ) ^ { 2 }$ 
C)  prime 
D)  $( \mathrm { z } + 7 ) ^ { 2 }$ 
A)  $( z + 7 ) ( z - 7 )$ 
B)  $( z - 7 ) ^ { 2 }$ 
C)  prime 
D)  $( \mathrm { z } + 7 ) ^ { 2 }$ A

Question 4

Factor completely.
-x5 + 6x4 + 8x3

Accepted Answer

A)  x3(x - 2)(x + 4) 
B)  x2(x2 + 6x + 8) 
C)  x3(x + 2)(x - 4) 
D)  x3(x + 2)(x + 4) 
A)  x3(x - 2)(x + 4) 
B)  x2(x2 + 6x + 8) 
C)  x3(x + 2)(x - 4) 
D)  x3(x + 2)(x + 4)

Question 5

Factor out the GCF from the polynomial.
-$$17 x ^ { 4 } - 13 x ^ { 6 }$$

Accepted Answer

A)  $17 x ^ { 4 } \left( 1 - \frac { 13 } { 17 } x ^ { 2 } \right)$ 
B)  $17 \left( x ^ { 4 } - 221 \right)$ 
C)  $x ^ { 4 } \left( 17 - 13 x ^ { 2 } \right)$ 
D)  $x ^ { 4 } \left( 1 - 13 x ^ { 2 } \right)$ 
A)  $17 x ^ { 4 } \left( 1 - \frac { 13 } { 17 } x ^ { 2 } \right)$ 
B)  $17 \left( x ^ { 4 } - 221 \right)$ 
C)  $x ^ { 4 } \left( 17 - 13 x ^ { 2 } \right)$ 
D)  $x ^ { 4 } \left( 1 - 13 x ^ { 2 } \right)$

Question 6

Factor the polynomial using the greatest common binomial factor.
-$$x \left( y ^ { 2 } - 12 \right) + 7 \left( y ^ { 2 } - 12 \right)$$

Accepted Answer

A)  $7 x \left( y ^ { 2 } - 12 \right)$ 
B)  $\left( y ^ { 2 } - 12 \right) ( x + 7 )$ 
C)  $\left( x y ^ { 2 } - 12 x \right) + \left( 7 y ^ { 2 } - 84 \right)$ 
D)  $\left( y ^ { 2 } - 12 \right) ( x - 7 )$ 
A)  $7 x \left( y ^ { 2 } - 12 \right)$ 
B)  $\left( y ^ { 2 } - 12 \right) ( x + 7 )$ 
C)  $\left( x y ^ { 2 } - 12 x \right) + \left( 7 y ^ { 2 } - 84 \right)$ 
D)  $\left( y ^ { 2 } - 12 \right) ( x - 7 )$

Question 7

Find the greatest common factor of the monomials.
-$15 y ^ { 4 } , 135 y ^ { 7 }$, and $225 y ^ { 5 }$

Accepted Answer

A)  $15 y ^ { 3 }$ 
B)  $2025 \mathrm { y } ^ { 3 }$ 
C)  $15 y ^ { 4 }$ 
D)  $135 y ^ { 4 }$ 
A)  $15 y ^ { 3 }$ 
B)  $2025 \mathrm { y } ^ { 3 }$ 
C)  $15 y ^ { 4 }$ 
D)  $135 y ^ { 4 }$

Question 8

Factor by grouping.
-$$x ^ { 2 } - 3 x - 3 x + 9$$

Accepted Answer

A)  $( x - 3 ) ( x - 3 )$ 
B)  $( x - 3 ) ( x + 6 )$ 
C)  $( x + 3 ) ( x - 3 )$ 
D)  $- 6 x \left( x ^ { 2 } + 9 \right)$ 
A)  $( x - 3 ) ( x - 3 )$ 
B)  $( x - 3 ) ( x + 6 )$ 
C)  $( x + 3 ) ( x - 3 )$ 
D)  $- 6 x \left( x ^ { 2 } + 9 \right)$

Question 9

Factor the polynomial using the greatest common binomial factor.
-$$9 x ( x - y ) + ( x - y )$$

Accepted Answer

A)  $9 x ( x - y )$ 
B)  $10 x ( a - y )$ 
C)  $\left( 9 x ^ { 2 } + 9 y \right) + ( x - y )$ 
D)  $( x - y ) ( 9 x + 1 )$ 
A)  $9 x ( x - y )$ 
B)  $10 x ( a - y )$ 
C)  $\left( 9 x ^ { 2 } + 9 y \right) + ( x - y )$ 
D)  $( x - y ) ( 9 x + 1 )$

Question 10

Find the greatest common factor of the monomials.
-$x ^ { 2 } y ^ { 7 } , x ^ { 3 } y ^ { 5 }$, and $x ^ { 4 } y ^ { 6 }$

Accepted Answer

A)  $x ^ { 5 } y ^ { 2 }$ 
B)  $x ^ { 2 } y ^ { 6 }$ 
C)  $x ^ { 2 } y ^ { 5 }$ 
D)  $x y$ 
A)  $x ^ { 5 } y ^ { 2 }$ 
B)  $x ^ { 2 } y ^ { 6 }$ 
C)  $x ^ { 2 } y ^ { 5 }$ 
D)  $x y$

Question 11

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime.
-$$2 x ^ { 2 } + 23 x + 11$$

Accepted Answer

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

Question 12

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is
prime.
-$$8 z ^ { 2 } + 6 z - 9$$

Accepted Answer

A)  $( 8 z + 3 ) ( z - 3 )$ 
B)  $( 2 z - 3 ) ( 4 z + 3 )$ 
C)  $( 2 z + 3 ) ( 4 z - 3 )$ 
D)  prime 
A)  $( 8 z + 3 ) ( z - 3 )$ 
B)  $( 2 z - 3 ) ( 4 z + 3 )$ 
C)  $( 2 z + 3 ) ( 4 z - 3 )$ 
D)  prime

Question 13

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is
prime.
-$10 y ^ { 2 } + 45 y - 25$

Accepted Answer

A)  $( 10 y - 5 ) ( y + 5 )$ 
B)  $5 ( 2 y + 1 ) ( y - 5 )$ 
C)  $5 ( 2 y - 1 ) ( y + 5 )$ 
D)  prime 
A)  $( 10 y - 5 ) ( y + 5 )$ 
B)  $5 ( 2 y + 1 ) ( y - 5 )$ 
C)  $5 ( 2 y - 1 ) ( y + 5 )$ 
D)  prime

Question 14

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

Accepted Answer

A)  $\left( x ^ { 3 } + 4 \right) ( 4 x - 1 )$ 
B)  $\left( x ^ { 3 } + 4 \right) ( x - 1 )$ 
C)  $\left( x ^ { 3 } - 1 \right) ( x + 4 )$ 
D)  $\left( x ^ { 3 } - 4 \right) ( x - 1 )$ 
A)  $\left( x ^ { 3 } + 4 \right) ( 4 x - 1 )$ 
B)  $\left( x ^ { 3 } + 4 \right) ( x - 1 )$ 
C)  $\left( x ^ { 3 } - 1 \right) ( x + 4 )$ 
D)  $\left( x ^ { 3 } - 4 \right) ( x - 1 )$

Question 15

Factor out the GCF from the polynomial.
-$3 x ^ { 4 } - 24 x ^ { 2 }$

Accepted Answer

A)  $x ^ { 4 } \left( 3 x ^ { 2 } - 24 \right)$ 
B)  $3 x ^ { 2 } \left( x ^ { 2 } - 8 \right)$ 
C)  $3 \left( x ^ { 4 } - 8 x ^ { 2 } \right)$ 
D)  $3 x ^ { 3 } ( x - 8 x )$ 
A)  $x ^ { 4 } \left( 3 x ^ { 2 } - 24 \right)$ 
B)  $3 x ^ { 2 } \left( x ^ { 2 } - 8 \right)$ 
C)  $3 \left( x ^ { 4 } - 8 x ^ { 2 } \right)$ 
D)  $3 x ^ { 3 } ( x - 8 x )$

Question 16

Factor out the GCF from the polynomial.
-$14 y ^ { 3 } - 6 y ^ { 2 } + 10 y$

Accepted Answer

A)  $2 \left( 7 y ^ { 3 } - 3 y ^ { 2 } + 5 y \right)$ 
B)  $2 y \left( 7 y ^ { 3 } - 3 y ^ { 2 } + 5 y \right)$ 
C)  $2 y \left( 7 y ^ { 2 } - 3 y + 5 \right)$ 
D)  $y \left( 14 y ^ { 2 } - 6 y + 10 \right)$ 
A)  $2 \left( 7 y ^ { 3 } - 3 y ^ { 2 } + 5 y \right)$ 
B)  $2 y \left( 7 y ^ { 3 } - 3 y ^ { 2 } + 5 y \right)$ 
C)  $2 y \left( 7 y ^ { 2 } - 3 y + 5 \right)$ 
D)  $y \left( 14 y ^ { 2 } - 6 y + 10 \right)$

Question 17

Factor the polynomial using the negative of the greatest common factor.
-$$- 14 x ^ { 4 } + 4 x ^ { 3 } - 10 x ^ { 2 }$$

Accepted Answer

A)  $2 x ^ { 2 } \left( - 7 x ^ { 2 } + 2 x - 5 \right)$ 
B)  $- 2 x ^ { 2 } \left( 7 x ^ { 2 } + 2 x - 5 \right)$ 
C)  $- 2 x \left( 7 x ^ { 3 } - 2 x ^ { 2 } + 5 x \right)$ 
D)  $- 2 x ^ { 2 } \left( 7 x ^ { 2 } - 2 x + 5 \right)$ 
A)  $2 x ^ { 2 } \left( - 7 x ^ { 2 } + 2 x - 5 \right)$ 
B)  $- 2 x ^ { 2 } \left( 7 x ^ { 2 } + 2 x - 5 \right)$ 
C)  $- 2 x \left( 7 x ^ { 3 } - 2 x ^ { 2 } + 5 x \right)$ 
D)  $- 2 x ^ { 2 } \left( 7 x ^ { 2 } - 2 x + 5 \right)$

Question 18

Factor the polynomial using the greatest common binomial factor.
-$$x y ( x - 4 ) + ( x - 4 )$$

Accepted Answer

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

Question 19

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime.
-$$12 z ^ { 2 } - 7 z - 12$$

Accepted Answer

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

Question 20

Factor completely.
-x3 - x2 - 12x

Accepted Answer

A)  prime 
B)  (x2 + 1)(x - 12) 
C)  x(x + 3)(x - 4) 
D)  x(x + 4)(x - 3) 
A)  prime 
B)  (x2 + 1)(x - 12) 
C)  x(x + 3)(x - 4) 
D)  x(x + 4)(x - 3)

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - $12 x ^ { 2 } + 25 x t + 12 t ^ { 2 }$

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - $2 x ^ { 2 } - 7 x - 15$

Factor completely. If unfactorable, indicate that the polynomial is prime. - $\mathrm { z } ^ { 2 } - 49$

Factor completely. -x5 + 6x4 + 8x3

Factor out the GCF from the polynomial. - $17 x ^ { 4 } - 13 x ^ { 6 }$

Factor the polynomial using the greatest common binomial factor. - $x \left( y ^ { 2 } - 12 \right) + 7 \left( y ^ { 2 } - 12 \right)$

Find the greatest common factor of the monomials. - $15 y ^ { 4 } , 135 y ^ { 7 }$ , and $225 y ^ { 5 }$

Factor by grouping. - $x ^ { 2 } - 3 x - 3 x + 9$

Factor the polynomial using the greatest common binomial factor. - $9 x ( x - y ) + ( x - y )$

Find the greatest common factor of the monomials. - $x ^ { 2 } y ^ { 7 } , x ^ { 3 } y ^ { 5 }$ , and $x ^ { 4 } y ^ { 6 }$

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - $2 x ^ { 2 } + 23 x + 11$

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - $8 z ^ { 2 } + 6 z - 9$

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - $10 y ^ { 2 } + 45 y - 25$

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

Factor out the GCF from the polynomial. - $3 x ^ { 4 } - 24 x ^ { 2 }$

Factor out the GCF from the polynomial. - $14 y ^ { 3 } - 6 y ^ { 2 } + 10 y$

Factor the polynomial using the negative of the greatest common factor. - $- 14 x ^ { 4 } + 4 x ^ { 3 } - 10 x ^ { 2 }$

Factor the polynomial using the greatest common binomial factor. - $x y ( x - 4 ) + ( x - 4 )$

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - $12 z ^ { 2 } - 7 z - 12$

Factor completely. -x³ - x² - 12x

Variables, Real Numbers, and Mathematical Models

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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. - 12x2+25xt+12t212 x ^ { 2 } + 25 x t + 12 t ^ { 2 }12x2+25xt+12t2

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - 2x2−7x−152 x ^ { 2 } - 7 x - 152x2−7x−15

Factor completely. If unfactorable, indicate that the polynomial is prime. - z2−49\mathrm { z } ^ { 2 } - 49z2−49

Factor completely. -x5 + 6x4 + 8x3

Factor out the GCF from the polynomial. - 17x4−13x617 x ^ { 4 } - 13 x ^ { 6 }17x4−13x6

Factor the polynomial using the greatest common binomial factor. - x(y2−12)+7(y2−12)x \left( y ^ { 2 } - 12 \right) + 7 \left( y ^ { 2 } - 12 \right)x(y2−12)+7(y2−12)

Find the greatest common factor of the monomials. - 15y4,135y715 y ^ { 4 } , 135 y ^ { 7 }15y4,135y7 , and 225y5225 y ^ { 5 }225y5

Factor by grouping. - x2−3x−3x+9x ^ { 2 } - 3 x - 3 x + 9x2−3x−3x+9

Factor the polynomial using the greatest common binomial factor. - 9x(x−y)+(x−y)9 x ( x - y ) + ( x - y )9x(x−y)+(x−y)

Find the greatest common factor of the monomials. - x2y7,x3y5x ^ { 2 } y ^ { 7 } , x ^ { 3 } y ^ { 5 }x2y7,x3y5 , and x4y6x ^ { 4 } y ^ { 6 }x4y6

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - 2x2+23x+112 x ^ { 2 } + 23 x + 112x2+23x+11

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - 8z2+6z−98 z ^ { 2 } + 6 z - 98z2+6z−9

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - 10y2+45y−2510 y ^ { 2 } + 45 y - 2510y2+45y−25

Factor by grouping. - x4−x3+4x−4x ^ { 4 } - x ^ { 3 } + 4 x - 4x4−x3+4x−4

Factor out the GCF from the polynomial. - 3x4−24x23 x ^ { 4 } - 24 x ^ { 2 }3x4−24x2

Factor out the GCF from the polynomial. - 14y3−6y2+10y14 y ^ { 3 } - 6 y ^ { 2 } + 10 y14y3−6y2+10y

Factor the polynomial using the negative of the greatest common factor. - −14x4+4x3−10x2- 14 x ^ { 4 } + 4 x ^ { 3 } - 10 x ^ { 2 }−14x4+4x3−10x2

Factor the polynomial using the greatest common binomial factor. - xy(x−4)+(x−4)x y ( x - 4 ) + ( x - 4 )xy(x−4)+(x−4)

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - 12z2−7z−1212 z ^ { 2 } - 7 z - 1212z2−7z−12

Factor completely. -x3 - x2 - 12x