Question 1

Factor completely. If unfactorable, indicate that the polynomial is prime.
-(a + b) x2 - 4(a + b) x - 60(a + b)

Accepted Answer

A)   (a + b) (x + 6) (x - 10) 
B)   prime
C)   (ax + 6b) (ax - 10b) 
D)   (a +b) (x - 6) (x + 10) E) None of the above
F) A) and C)

Question 2

Factor the polynomial using the negative of the greatest common factor.
- −5x4−15x3+10x2- 5 x ^ { 4 } - 15 x ^ { 3 } + 10 x ^ { 2 }−5x4−15x3+10x2

Accepted Answer

A)    5x2(−x2−3x+2) 5 x ^ { 2 } \left( - x ^ { 2 } - 3 x + 2 \right) 5x2(−x2−3x+2)  
B)    −5x2(x2−3x+2) - 5 x ^ { 2 } \left( x ^ { 2 } - 3 x + 2 \right) −5x2(x2−3x+2)  
C)    −5x(x3+3x2−2x) - 5 x \left( x ^ { 3 } + 3 x ^ { 2 } - 2 x \right) −5x(x3+3x2−2x)  
D)    −5x2(x2+3x−2) - 5 x ^ { 2 } \left( x ^ { 2 } + 3 x - 2 \right) −5x2(x2+3x−2) E) All of the above
F) None of the above

Question 3

Factor the polynomial using the greatest common binomial factor.
- 14(y+10) −x(y+10) 14 ( y + 10 )  - x ( y + 10 ) 14(y+10) −x(y+10)

Accepted Answer

A)    (14y+140) −(xy+10x) ( 14 y + 140 )  - ( x y + 10 x ) (14y+140) −(xy+10x)  
B)    (y+10) (14+x) ( y + 10 )  ( 14 + x ) (y+10) (14+x)  
C)    (y+10) (14−x) ( \mathrm { y } + 10 )  ( 14 - \mathrm { x } ) (y+10) (14−x)  
D)    (y−10) (x−14) ( \mathrm { y } - 10 )  ( \mathrm { x } - 14 ) (y−10) (x−14) E) A) and B)
F) All of the above

Question 4

Factor the polynomial using the negative of the greatest common factor.
- −14a3b2−21ab- 14 a ^ { 3 } b ^ { 2 } - 21 a b−14a3b2−21ab

Accepted Answer

A)    −7ab(2a2b+3) - 7 a b \left( 2 a ^ { 2 } b + 3 \right) −7ab(2a2b+3)  
B)    −7a(2a2b2+3b) - 7 a \left( 2 a ^ { 2 } b ^ { 2 } + 3 b \right) −7a(2a2b2+3b)  
C)    7ab(−2a2b−3) 7 a b \left( - 2 a ^ { 2 } b - 3 \right) 7ab(−2a2b−3)  
D)    −7ab(2a2b−3) - 7 a b \left( 2 a ^ { 2 } b - 3 \right) −7ab(2a2b−3) E) All of the above
F) A) and B)

Question 5

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is
prime.
- 3x2+13x−203 x ^ { 2 } + 13 x - 203x2+13x−20

Accepted Answer

A)    (3x−4) (x+5) ( 3 x - 4 )  ( x + 5 ) (3x−4) (x+5)  
B)    (3x+5) (x−4) ( 3 x + 5 )  ( x - 4 ) (3x+5) (x−4)  
C)    (3x+4) (x−5) ( 3 x + 4 )  ( x - 5 ) (3x+4) (x−5)  
D)   prime E) A) and D)
F) B) and D)

Question 6

Factor the polynomial using the negative of the greatest common factor.
- −28a2b3+12ab- 28 a ^ { 2 } b ^ { 3 } + 12 a b−28a2b3+12ab

Accepted Answer

A)    4ab(−7ab2+3) 4 a b \left( - 7 a b ^ { 2 } + 3 \right) 4ab(−7ab2+3)  
B)    −4a(7ab3−3b) - 4 a \left( 7 a b ^ { 3 } - 3 b \right) −4a(7ab3−3b)  
C)    −4ab(7ab2−3) - 4 a b \left( 7 a b ^ { 2 } - 3 \right) −4ab(7ab2−3)  
D)    −4ab(7ab2+3) - 4 a b \left( 7 a b ^ { 2 } + 3 \right) −4ab(7ab2+3) E) A) and B)
F) None of the above

Question 7

Find the greatest common factor of the monomials.
- 2x22 x ^ { 2 }2x2  and 12

Accepted Answer

A)   6
B)    2x22 x ^ { 2 }2x2 
C)   2
D)    2x2 x2xE) None of the above
F) B) and C)

Question 8

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

Accepted Answer

A)   prime
B)    −2(3x−2) (2x+3) - 2 ( 3 x - 2 )  ( 2 x + 3 ) −2(3x−2) (2x+3)  
C)    (−6x+4) (2x+3) ( - 6 x + 4 )  ( 2 x + 3 ) (−6x+4) (2x+3)  
D)    −2(3x+2) (2x−3) - 2 ( 3 x + 2 )  ( 2 x - 3 ) −2(3x+2) (2x−3) E) B) and C)
F) A) and C)

Question 9

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is
prime.
- 9y2+18y+89 y ^ { 2 } + 18 y + 89y2+18y+8

Accepted Answer

A)    (9y+2) (y+4) ( 9 y + 2 )  ( y + 4 ) (9y+2) (y+4)  
B)    (3y+2) (3y+4) ( 3 y + 2 )  ( 3 y + 4 ) (3y+2) (3y+4)  
C)    (3y−2) (3y−4) ( 3 y - 2 )  ( 3 y - 4 ) (3y−2) (3y−4)  
D)   prime E) B) and C)
F) C) and D)

Question 10

Factor by grouping.
- 12x2+15xy−8xy−10y212 x ^ { 2 } + 15 x y - 8 x y - 10 y ^ { 2 }12x2+15xy−8xy−10y2

Accepted Answer

A)    (12x−2y) (x+5y) ( 12 x - 2 y )  ( x + 5 y ) (12x−2y) (x+5y)  
B)    (3x+2y) (4x+5y) ( 3 x + 2 y )  ( 4 x + 5 y ) (3x+2y) (4x+5y)  
C)    (3x−2) (4x+5) ( 3 x - 2 )  ( 4 x + 5 ) (3x−2) (4x+5)  
D)    (3x−2y) (4x+5y) ( 3 x - 2 y )  ( 4 x + 5 y ) (3x−2y) (4x+5y) E) B) and D)
F) C) and D)

Question 11

Solve the problem.
-The length and area of the rectangle are given. Express the width as a binomial.

Accepted Answer

A)    3x−33 x - 33x−3 
B)    2x+42 x + 42x+4 
C)    3x−43 x - 43x−4 
D)   Not enough information. E) A) and B)
F) None of the above

Question 12

Find the greatest common factor of the monomials.
- 64x8y464 x ^ { 8 } y ^ { 4 }64x8y4  and  88x5y888 x ^ { 5 } y ^ { 8 }88x5y8

Accepted Answer

A)    704x8y8704 x ^ { 8 } y ^ { 8 }704x8y8 
B)    8x8y88 x ^ { 8 } y ^ { 8 }8x8y8 
C)    4x3y44 x ^ { 3 } y ^ { 4 }4x3y4 
D)    8x5y48 x ^ { 5 } y ^ { 4 }8x5y4E) C) and D)
F) A) and B)

Question 13

Factor the polynomial using the greatest common binomial factor.
- x(x−5) +11(x−5) x ( x - 5 )  + 11 ( x - 5 ) x(x−5) +11(x−5)

Accepted Answer

A)    (x2−5x) (11x−55) \left( x ^ { 2 } - 5 x \right)  ( 11 x - 55 ) (x2−5x) (11x−55)  
B)    (x+5) (x−11) ( x + 5 )  ( x - 11 ) (x+5) (x−11)  
C)    (x−5) (x−11) ( x - 5 )  ( x - 11 ) (x−5) (x−11)  
D)    (x−5) (x+11) ( x - 5 )  ( x + 11 ) (x−5) (x+11) E) A) and B)
F) A) and C)

Question 14

Factor the polynomial using the greatest common binomial factor.
- x2(x−7) −2(x−7) x ^ { 2 } ( x - 7 )  - 2 ( x - 7 ) x2(x−7) −2(x−7)

Accepted Answer

A)    x2(x−7) x ^ { 2 } ( x - 7 ) x2(x−7)  
B)    (x−7) (x2+1) ( x - 7 )  \left( x ^ { 2 } + 1 \right) (x−7) (x2+1)  
C)    (x3−7x2) −(x−7) \left( x ^ { 3 } - 7 x ^ { 2 } \right)  - ( x - 7 ) (x3−7x2) −(x−7)  
D)    (x−7) (x2−2) ( x - 7 )  \left( x ^ { 2 } - 2 \right) (x−7) (x2−2) E) B) and C)
F) A) and D)

Question 15

Factor the polynomial using the greatest common binomial factor.
- x(y−8) −4(y−8) x ( y - 8 )  - 4 ( y - 8 ) x(y−8) −4(y−8)

Accepted Answer

A)    (y−8) (x+4) ( y - 8 )  ( x + 4 ) (y−8) (x+4)  
B)    4x(y−8) 4 x ( y - 8 ) 4x(y−8)  
C)    (xy−8x) (4y−32) ( x y - 8 x )  ( 4 y - 32 ) (xy−8x) (4y−32)  
D)    (y−8) (x−4) ( y - 8 )  ( x - 4 ) (y−8) (x−4) E) C) and D)
F) A) and C)

Question 16

Write a polynomial for the width of the rectangle.
-Write a polynomial for the width of the rectangle.

Accepted Answer

A)    4+3x44 + 3 x ^ { 4 }4+3x4 
B)    4x+3x44 x + 3 x ^ { 4 }4x+3x4 
C)    x+3x4x + 3 x ^ { 4 }x+3x4 
D)    18x+18x518 x + 18 x ^ { 5 }18x+18x5E) C) and D)
F) B) and D)

Question 17

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime.
- 6x2−5xt−4t26 x ^ { 2 } - 5 x t - 4 t ^ { 2 }6x2−5xt−4t2

Accepted Answer

A)    (2x−t) (3x+4t) ( 2 x - t )  ( 3 x + 4 t ) (2x−t) (3x+4t)  
B)   prime
C)    (6x+t) (x−4t) ( 6 x + t )  ( x - 4 t ) (6x+t) (x−4t)  
D)    (2x+t) (3x−4t) ( 2 x + t )  ( 3 x - 4 t ) (2x+t) (3x−4t) E) None of the above
F) A) and B)

Question 18

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime.
- 25x3y4+35x2y5+12xy625 x ^ { 3 } y ^ { 4 } + 35 x ^ { 2 } y ^ { 5 } + 12 x y ^ { 6 }25x3y4+35x2y5+12xy6

Accepted Answer

A)    xy4(5x+3y) (5x+4y) x y ^ { 4 } ( 5 x + 3 y )  ( 5 x + 4 y ) xy4(5x+3y) (5x+4y)  
B)    x(5xy4+3y5) (5x+4y) x \left( 5 x y ^ { 4 } + 3 y ^ { 5 } \right)  ( 5 x + 4 y ) x(5xy4+3y5) (5x+4y)  
C)    y4(5x+3y) (5x2+4xy) y ^ { 4 } ( 5 x + 3 y )  \left( 5 x ^ { 2 } + 4 x y \right) y4(5x+3y) (5x2+4xy)  
D)   prime E) A) and B)
F) B) and C)

Question 19

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

Accepted Answer

A)    (4z−3) (2z+3) ( 4 z - 3 )  ( 2 z + 3 ) (4z−3) (2z+3)  
B)    (4z+3) (2z−3) ( 4 z + 3 )  ( 2 z - 3 ) (4z+3) (2z−3)  
C)   prime
D)    (8z−3) (z+3) ( 8 \mathrm { z } - 3 )  ( \mathrm { z } + 3 ) (8z−3) (z+3) E) None of the above
F) A) and D)

Question 20

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime.
- 36x2+21xy+3y236 x ^ { 2 } + 21 x y + 3 y ^ { 2 }36x2+21xy+3y2

Accepted Answer

A)    3(3x+y) (4x+y) 3 ( 3 x + y )  ( 4 x + y ) 3(3x+y) (4x+y)  
B)   prime
C)    3(3x−y) (4x−y) 3 ( 3 x - y )  ( 4 x - y ) 3(3x−y) (4x−y)  
D)    (9x+3y) (4x+y) ( 9 x + 3 y )  ( 4 x + y ) (9x+3y) (4x+y) E) A) and B)
F) A) and C)

Exam 6: Factoring Polynomials

Factor the polynomial using the greatest common binomial factor. - x(y−8) −4(y−8) x ( y - 8 ) - 4 ( y - 8 ) x(y−8) −4(y−8)

Correct AnswerverifiedShow Answer

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - 36x2+21xy+3y236 x ^ { 2 } + 21 x y + 3 y ^ { 2 }36x2+21xy+3y2

Correct AnswerverifiedShow Answer

Find the greatest common factor of the monomials. - 2x22 x ^ { 2 }2x2 and 12

Correct AnswerverifiedShow Answer

Find the greatest common factor of the monomials. - 64x8y464 x ^ { 8 } y ^ { 4 }64x8y4 and 88x5y888 x ^ { 5 } y ^ { 8 }88x5y8

Correct AnswerverifiedShow Answer

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - 25x3y4+35x2y5+12xy625 x ^ { 3 } y ^ { 4 } + 35 x ^ { 2 } y ^ { 5 } + 12 x y ^ { 6 }25x3y4+35x2y5+12xy6

Correct AnswerverifiedShow Answer

Factor the polynomial using the negative of the greatest common factor. - −14a3b2−21ab- 14 a ^ { 3 } b ^ { 2 } - 21 a b−14a3b2−21ab

Correct AnswerverifiedShow Answer

Factor the polynomial using the greatest common binomial factor. - x(x−5) +11(x−5) x ( x - 5 ) + 11 ( x - 5 ) x(x−5) +11(x−5)

Correct AnswerverifiedShow Answer

Factor the polynomial using the negative of the greatest common factor. - −5x4−15x3+10x2- 5 x ^ { 4 } - 15 x ^ { 3 } + 10 x ^ { 2 }−5x4−15x3+10x2

Correct AnswerverifiedShow Answer

Factor completely. If unfactorable, indicate that the polynomial is prime. -(a + b) x2 - 4(a + b) x - 60(a + b)

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - 3x2+13x−203 x ^ { 2 } + 13 x - 203x2+13x−20

Correct AnswerverifiedShow Answer

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - 6x2−5xt−4t26 x ^ { 2 } - 5 x t - 4 t ^ { 2 }6x2−5xt−4t2

Correct AnswerverifiedShow Answer

Write a polynomial for the width of the rectangle. -Write a polynomial for the width of the rectangle.

Correct AnswerverifiedShow Answer

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - 9y2+18y+89 y ^ { 2 } + 18 y + 89y2+18y+8

Correct AnswerverifiedShow Answer

Factor the polynomial using the greatest common binomial factor. - 14(y+10) −x(y+10) 14 ( y + 10 ) - x ( y + 10 ) 14(y+10) −x(y+10)

Correct AnswerverifiedShow Answer

Factor the polynomial using the greatest common binomial factor. - x2(x−7) −2(x−7) x ^ { 2 } ( x - 7 ) - 2 ( x - 7 ) x2(x−7) −2(x−7)

Correct AnswerverifiedShow Answer

Factor the polynomial using the negative of the greatest common factor. - −28a2b3+12ab- 28 a ^ { 2 } b ^ { 3 } + 12 a b−28a2b3+12ab

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

Solve the problem. -The length and area of the rectangle are given. Express the width as a binomial.

Correct AnswerverifiedShow Answer

Factor by grouping. - 12x2+15xy−8xy−10y212 x ^ { 2 } + 15 x y - 8 x y - 10 y ^ { 2 }12x2+15xy−8xy−10y2

Correct AnswerverifiedShow Answer

Factor the polynomial using the greatest common binomial factor. - $x ( y - 8 ) - 4 ( y - 8 )$

Correct Answer
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Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - $36 x ^ { 2 } + 21 x y + 3 y ^ { 2 }$

Correct Answer
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Find the greatest common factor of the monomials. - $2 x ^ { 2 }$ and 12

Correct Answer
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Find the greatest common factor of the monomials. - $64 x ^ { 8 } y ^ { 4 }$ and $88 x ^ { 5 } y ^ { 8 }$

Correct Answer
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Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - $25 x ^ { 3 } y ^ { 4 } + 35 x ^ { 2 } y ^ { 5 } + 12 x y ^ { 6 }$

Correct Answer
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Factor the polynomial using the negative of the greatest common factor. - $- 14 a ^ { 3 } b ^ { 2 } - 21 a b$

Correct Answer
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Factor the polynomial using the greatest common binomial factor. - $x ( x - 5 ) + 11 ( x - 5 )$

Correct Answer
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Factor the polynomial using the negative of the greatest common factor. - $- 5 x ^ { 4 } - 15 x ^ { 3 } + 10 x ^ { 2 }$

Correct Answer
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Factor completely. If unfactorable, indicate that the polynomial is prime. -(a + b) x² - 4(a + b) x - 60(a + b)

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

Correct Answer
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Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - $3 x ^ { 2 } + 13 x - 20$

Correct Answer
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Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - $6 x ^ { 2 } - 5 x t - 4 t ^ { 2 }$

Correct Answer
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Write a polynomial for the width of the rectangle. -Write a polynomial for the width of the rectangle. $Write a polynomial for the width of the rectangle. -Write a polynomial for the width of the rectangle. A) 4 + 3 x ^ { 4 } B) 4 x + 3 x ^ { 4 } C) x + 3 x ^ { 4 } D) 18 x + 18 x ^ { 5 }$

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

Correct Answer
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Factor the polynomial using the greatest common binomial factor. - $14 ( y + 10 ) - x ( y + 10 )$

Correct Answer
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Factor the polynomial using the greatest common binomial factor. - $x ^ { 2 } ( x - 7 ) - 2 ( x - 7 )$

Correct Answer
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Factor the polynomial using the negative of the greatest common factor. - $- 28 a ^ { 2 } b ^ { 3 } + 12 a b$

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

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

Correct Answer
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