Question 1

Factor by grouping.
-$8 x ^ { 2 } + 10 x + 12 x + 15$

Accepted Answer

A)  $( 2 x - 3 ) ( 4 x - 5 )$ 
B)  $( 2 x + 3 ) ( 4 x + 5 )$ 
C)  $( 8 x + 3 ) ( x + 5 )$ 
D)  $( 8 x - 3 ) ( x - 5 )$ 
A)  $( 2 x - 3 ) ( 4 x - 5 )$ 
B)  $( 2 x + 3 ) ( 4 x + 5 )$ 
C)  $( 8 x + 3 ) ( x + 5 )$ 
D)  $( 8 x - 3 ) ( x - 5 )$

Question 2

Factor completely.
-5x2- 25x + 30

Accepted Answer

A)  prime 
B)  (x - 2)(5x - 15) 
C)  5(x - 2)(x - 3) 
D)  5(x - 6)(x + 1) 
A)  prime 
B)  (x - 2)(5x - 15) 
C)  5(x - 2)(x - 3) 
D)  5(x - 6)(x + 1)

Question 3

Factor completely.
-x2(y - 5) - 12x(y - 5) + 20(y - 5)

Accepted Answer

A)  (x + 10)(x + 2)(y - 5) 
B)  (x - 10)(x - 2)(y - 5) 
C)  (x + 10)(x - 2)(y - 5) 
D)  (x - 10)(x + 2)(y - 5) 
A)  (x + 10)(x + 2)(y - 5) 
B)  (x - 10)(x - 2)(y - 5) 
C)  (x + 10)(x - 2)(y - 5) 
D)  (x - 10)(x + 2)(y - 5)

Question 4

Factor completely.
-2x2- 2x - 12

Accepted Answer

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

Question 5

Factor by grouping.
-$$10 x ^ { 3 } - 12 x ^ { 2 } y - 25 x y ^ { 2 } + 30 y ^ { 3 }$$

Accepted Answer

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

Question 6

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is
prime.
-8x2y2 - 30xy2 + 25y2

Accepted Answer

A)  y2(x - 5)(8x - 5) 
B)  y2(4x - 5)(2x - 5) 
C)  (2x - 5y)(4x - 5y) 
D)  (4x - 5y)(2x - 5y) 
A)  y2(x - 5)(8x - 5) 
B)  y2(4x - 5)(2x - 5) 
C)  (2x - 5y)(4x - 5y) 
D)  (4x - 5y)(2x - 5y)

Question 7

Factor out the GCF from the polynomial.
-$48 m ^ { 7 } - 108 m ^ { 5 } + 60 m ^ { 2 }$

Accepted Answer

A)  $12 \left( 4 m ^ { 7 } - 9 m ^ { 5 } + 5 m ^ { 2 } \right)$ 
B)  $12 m ^ { 2 } \left( 4 m ^ { 5 } - 9 m ^ { 3 } + 5 \right)$ 
C)  $- m ^ { 2 } \left( - 48 m ^ { 5 } - 108 m ^ { 3 } - 60 \right)$ 
D)  $m ^ { 2 } \left( 48 m ^ { 5 } - 108 m ^ { 3 } + 60 \right)$ 
A)  $12 \left( 4 m ^ { 7 } - 9 m ^ { 5 } + 5 m ^ { 2 } \right)$ 
B)  $12 m ^ { 2 } \left( 4 m ^ { 5 } - 9 m ^ { 3 } + 5 \right)$ 
C)  $- m ^ { 2 } \left( - 48 m ^ { 5 } - 108 m ^ { 3 } - 60 \right)$ 
D)  $m ^ { 2 } \left( 48 m ^ { 5 } - 108 m ^ { 3 } + 60 \right)$

Question 8

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime.
-$$12 x ^ { 2 } + 23 x + 10$$

Accepted Answer

A)  $( 3 x + 2 ) ( 4 x + 5 )$ 
B)  $( 4 x + 2 ) ( 3 x + 5 )$ 
C)  $( x + 2 ) ( 12 x + 5 )$ 
D)  $( 3 x - 2 ) ( 4 x - 5 )$ 
A)  $( 3 x + 2 ) ( 4 x + 5 )$ 
B)  $( 4 x + 2 ) ( 3 x + 5 )$ 
C)  $( x + 2 ) ( 12 x + 5 )$ 
D)  $( 3 x - 2 ) ( 4 x - 5 )$

Question 9

Factor out the GCF from the polynomial.
-$15 m ^ { 8 } + 9 m ^ { 4 } - 6 m ^ { 2 }$

Accepted Answer

A)  cannot be factored 
B)  $m ^ { 2 } \left( 15 m ^ { 6 } + 9 m ^ { 2 } - 6 \right)$ 
C)  $3 \left( 5 m ^ { 8 } + 3 m ^ { 4 } - 2 m ^ { 2 } \right)$ 
D)  $3 m ^ { 2 } \left( 5 m ^ { 6 } + 3 m ^ { 2 } - 2 \right)$ 
A)  cannot be factored 
B)  $m ^ { 2 } \left( 15 m ^ { 6 } + 9 m ^ { 2 } - 6 \right)$ 
C)  $3 \left( 5 m ^ { 8 } + 3 m ^ { 4 } - 2 m ^ { 2 } \right)$ 
D)  $3 m ^ { 2 } \left( 5 m ^ { 6 } + 3 m ^ { 2 } - 2 \right)$

Question 10

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is
prime.
-$9 x ^ { 2 } - 12 x t + 4 t ^ { 2 }$

Accepted Answer

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

Question 11

Factor the polynomial using the negative of the greatest common factor.
-$- 14 x ^ { 3 } y ^ { 2 } - 4 x ^ { 3 } y + 8 x ^ { 2 } y$

Accepted Answer

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

Question 12

Factor out the GCF from the polynomial.
-$$48 x ^ { 3 } y + 30 x y ^ { 5 }$$

Accepted Answer

A)  $6 x y \left( 8 x ^ { 2 } + 5 y ^ { 4 } \right)$ 
B)  $6 y \left( 8 x ^ { 3 } + 5 x y ^ { 4 } \right)$ 
C)  $6 x \left( 8 x ^ { 2 } y + 5 y ^ { 5 } \right)$ 
D)  $x y \left( 48 x ^ { 2 } + 30 y ^ { 4 } \right)$ 
A)  $6 x y \left( 8 x ^ { 2 } + 5 y ^ { 4 } \right)$ 
B)  $6 y \left( 8 x ^ { 3 } + 5 x y ^ { 4 } \right)$ 
C)  $6 x \left( 8 x ^ { 2 } y + 5 y ^ { 5 } \right)$ 
D)  $x y \left( 48 x ^ { 2 } + 30 y ^ { 4 } \right)$

Question 13

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is
prime.
-$20 x ^ { 2 } + 25 x + 5$

Accepted Answer

A)  $( x + 5 ) ( 20 x + 1 )$ 
B)  $( 5 x + 5 ) ( 4 x + 1 )$ 
C)  $( 4 x + 5 ) ( 5 x + 1 )$ 
D)  $( 5 x - 5 ) ( 4 x - 1 )$ 
A)  $( x + 5 ) ( 20 x + 1 )$ 
B)  $( 5 x + 5 ) ( 4 x + 1 )$ 
C)  $( 4 x + 5 ) ( 5 x + 1 )$ 
D)  $( 5 x - 5 ) ( 4 x - 1 )$

Question 14

Factor completely.
-u2 - 4uv - 21v2

Accepted Answer

A)  (u - 3v)(u + v) 
B)  (u + 3v)(u - 7v) 
C)  prime 
D)  (u - 3v)(u + 7v) 
A)  (u - 3v)(u + v) 
B)  (u + 3v)(u - 7v) 
C)  prime 
D)  (u - 3v)(u + 7v)

Question 15

Find the greatest common factor of the monomials.
-$88 x ^ { 2 }$ and $44 x ^ { 7 }$

Accepted Answer

A)  $66 x ^ { 2 }$ 
B)  $44 x ^ { 2 }$ 
C)  $88 x ^ { 2 }$ 
D)  $22 x ^ { 5 }$ 
A)  $66 x ^ { 2 }$ 
B)  $44 x ^ { 2 }$ 
C)  $88 x ^ { 2 }$ 
D)  $22 x ^ { 5 }$

Question 16

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime.
-$$- 12 x ^ { 2 } - 10 x + 12$$

Accepted Answer

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

Question 17

Write a polynomial for the length of the rectangle.
-

Accepted Answer

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

Question 18

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is
prime.
-$$6 x ^ { 2 } - 21 x - 12$$

Accepted Answer

A)  $3 ( 2 x - 1 ) ( x + 4 )$ 
B)  $3 ( 2 x + 1 ) ( x - 4 )$ 
C)  prime 
D)  $( 6 x - 3 ) ( x + 4 )$ 
A)  $3 ( 2 x - 1 ) ( x + 4 )$ 
B)  $3 ( 2 x + 1 ) ( x - 4 )$ 
C)  prime 
D)  $( 6 x - 3 ) ( x + 4 )$

Question 19

Find the greatest common factor of the monomials.
-$10 x ^ { 3 } y ^ { 6 } , 10 x ^ { 5 } y ^ { 5 }$, and $2 x ^ { 4 } y ^ { 4 }$

Accepted Answer

A)  $5 x ^ { 5 } y ^ { 6 }$ 
B)  $10 x ^ { 3 } y ^ { 4 }$ 
C)  $2 x ^ { 4 } y ^ { 3 }$ 
D)  $2 x ^ { 3 } y ^ { 4 }$ 
A)  $5 x ^ { 5 } y ^ { 6 }$ 
B)  $10 x ^ { 3 } y ^ { 4 }$ 
C)  $2 x ^ { 4 } y ^ { 3 }$ 
D)  $2 x ^ { 3 } y ^ { 4 }$

Question 20

Factor completely.
-x5 + 4x4 - 45x3

Accepted Answer

A)  x3(x - 5)(x + 9) 
B)  x3(x + 5)(x + 9) 
C)  x3(x - 5)(x - 9) 
D)  x-5(x2 + 4x - 45) 
A)  x3(x - 5)(x + 9) 
B)  x3(x + 5)(x + 9) 
C)  x3(x - 5)(x - 9) 
D)  x-5(x2 + 4x - 45)

Factor by grouping. - $8 x ^ { 2 } + 10 x + 12 x + 15$

Factor completely. -5x²- 25x + 30

Factor completely. -x²(y - 5) - 12x(y - 5) + 20(y - 5)

Factor completely. -2x²- 2x - 12

Factor by grouping. - $10 x ^ { 3 } - 12 x ^ { 2 } y - 25 x y ^ { 2 } + 30 y ^ { 3 }$

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is prime. -8x²y² - 30xy² + 25y²

Factor out the GCF from the polynomial. - $48 m ^ { 7 } - 108 m ^ { 5 } + 60 m ^ { 2 }$

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - $12 x ^ { 2 } + 23 x + 10$

Factor out the GCF from the polynomial. - $15 m ^ { 8 } + 9 m ^ { 4 } - 6 m ^ { 2 }$

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - $9 x ^ { 2 } - 12 x t + 4 t ^ { 2 }$

Factor the polynomial using the negative of the greatest common factor. - $- 14 x ^ { 3 } y ^ { 2 } - 4 x ^ { 3 } y + 8 x ^ { 2 } y$

Factor out the GCF from the polynomial. - $48 x ^ { 3 } y + 30 x y ^ { 5 }$

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - $20 x ^ { 2 } + 25 x + 5$

Factor completely. -u² - 4uv - 21v²

Find the greatest common factor of the monomials. - $88 x ^ { 2 }$ and $44 x ^ { 7 }$

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - $- 12 x ^ { 2 } - 10 x + 12$

Write a polynomial for the length of the rectangle. -

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - $6 x ^ { 2 } - 21 x - 12$

Find the greatest common factor of the monomials. - $10 x ^ { 3 } y ^ { 6 } , 10 x ^ { 5 } y ^ { 5 }$ , and $2 x ^ { 4 } y ^ { 4 }$

Factor completely. -x5 + 4x4 - 45x3

Variables, Real Numbers, and Mathematical Models

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Exam 6: Factoring Polynomials

Factor by grouping. - 8x2+10x+12x+158 x ^ { 2 } + 10 x + 12 x + 158x2+10x+12x+15

Factor completely. -5x2- 25x + 30

Factor completely. -x2(y - 5) - 12x(y - 5) + 20(y - 5)

Factor completely. -2x2- 2x - 12

Factor by grouping. - 10x3−12x2y−25xy2+30y310 x ^ { 3 } - 12 x ^ { 2 } y - 25 x y ^ { 2 } + 30 y ^ { 3 }10x3−12x2y−25xy2+30y3

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is prime. -8x2y2 - 30xy2 + 25y2

Factor out the GCF from the polynomial. - 48m7−108m5+60m248 m ^ { 7 } - 108 m ^ { 5 } + 60 m ^ { 2 }48m7−108m5+60m2

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - 12x2+23x+1012 x ^ { 2 } + 23 x + 1012x2+23x+10

Factor out the GCF from the polynomial. - 15m8+9m4−6m215 m ^ { 8 } + 9 m ^ { 4 } - 6 m ^ { 2 }15m8+9m4−6m2

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - 9x2−12xt+4t29 x ^ { 2 } - 12 x t + 4 t ^ { 2 }9x2−12xt+4t2

Factor the polynomial using the negative of the greatest common factor. - −14x3y2−4x3y+8x2y- 14 x ^ { 3 } y ^ { 2 } - 4 x ^ { 3 } y + 8 x ^ { 2 } y−14x3y2−4x3y+8x2y

Factor out the GCF from the polynomial. - 48x3y+30xy548 x ^ { 3 } y + 30 x y ^ { 5 }48x3y+30xy5

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - 20x2+25x+520 x ^ { 2 } + 25 x + 520x2+25x+5

Factor completely. -u2 - 4uv - 21v2

Find the greatest common factor of the monomials. - 88x288 x ^ { 2 }88x2 and 44x744 x ^ { 7 }44x7

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - −12x2−10x+12- 12 x ^ { 2 } - 10 x + 12−12x2−10x+12