Question 1

Factor the trinomial completely.
-$25 x ^ { 2 } y ^ { 2 } - 60 x ^ { 2 } y + 36 x ^ { 2 }$

Accepted Answer

A)  $x ^ { 2 } ( 5 y - 6 ) ^ { 2 }$ 
B)  $x ^ { 2 } ( 5 y - 6 ) ( 5 y + 6 )$ 
C)  $x ^ { 2 } ( 5 y + 6 ) ^ { 2 }$ 
D) prime 
A)  $x ^ { 2 } ( 5 y - 6 ) ^ { 2 }$ 
B)  $x ^ { 2 } ( 5 y - 6 ) ( 5 y + 6 )$ 
C)  $x ^ { 2 } ( 5 y + 6 ) ^ { 2 }$ 
D) prime

Question 2

Factor the four-term polynomial by grouping.
-xy + 12x - 4y - 48

Accepted Answer

A) (x - 12)(y + 4) 
B) (y + 12)(x - 4) 
C) (y - 12)(x + 4) 
D) (x + 12)(y - 4) 
A) (x - 12)(y + 4) 
B) (y + 12)(x - 4) 
C) (y - 12)(x + 4) 
D) (x + 12)(y - 4)

Question 3

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$x ^ { 2 } - 4 x - 32$

Accepted Answer

A) (x - 8)(x + 4) 
B) (x - 32)(x + 1) 
C) (x + 8)(x - 4) 
D) prime 
A) (x - 8)(x + 4) 
B) (x - 32)(x + 1) 
C) (x + 8)(x - 4) 
D) prime

Question 4

Factor the trinomial completely.
- $4 x ^ { 3 } y + 36 x ^ { 2 } y ^ { 2 } + 81 x y ^ { 3 }$

Accepted Answer

A)  $\left( 4 x ^ { 2 } y + x y \right) \left( x + 81 y ^ { 2 } \right)$ 
B)  $x y ( 2 x - 9 y ) ^ { 2 }$ 
C)  $x y ( 2 x + 9 y ) ^ { 2 }$ 
D)  $x y ( 2 x + 9 y ) ( 2 x - 9 y )$ 
A)  $\left( 4 x ^ { 2 } y + x y \right) \left( x + 81 y ^ { 2 } \right)$ 
B)  $x y ( 2 x - 9 y ) ^ { 2 }$ 
C)  $x y ( 2 x + 9 y ) ^ { 2 }$ 
D)  $x y ( 2 x + 9 y ) ( 2 x - 9 y )$

Question 5

Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$y ^ { 2 } + 50 y + 625$

Accepted Answer

A) (y + 25)(y - 25) 
B)  $( \mathrm { y } + 25 ) ^ { 2 }$ 
C)  $( \mathrm { y } - 25 ) ^ { 2 }$ 
D) Prime 
A) (y + 25)(y - 25) 
B)  $( \mathrm { y } + 25 ) ^ { 2 }$ 
C)  $( \mathrm { y } - 25 ) ^ { 2 }$ 
D) Prime

Question 6

Solve the equation.
-(7y + 9)(2y + 29)= 0

Accepted Answer

A) 2, 27 
B)  $\frac { 9 } { 7 } , \frac { 29 } { 2 }$ 
C)   $- \frac { 7 } { 2 } , - \frac { 2 } { 29 }$ 
D)   $- \frac { 9 } { 7 } , - \frac { 29 } { 2 }$ 
A) 2, 27 
B)  $\frac { 9 } { 7 } , \frac { 29 } { 2 }$ 
C)   $- \frac { 7 } { 2 } , - \frac { 2 } { 29 }$ 
D)   $- \frac { 9 } { 7 } , - \frac { 29 } { 2 }$

Question 7

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-  $- x ^ { 2 } - 3 x + 40$

Accepted Answer

A) -1(x - 8)(x + 1) 
B) -1(x - 8)(x + 5) 
C) -1(x + 8)(x - 5) 
D) -1(x - 8)(x - 5) 
A) -1(x - 8)(x + 1) 
B) -1(x - 8)(x + 5) 
C) -1(x + 8)(x - 5) 
D) -1(x - 8)(x - 5)

Question 8

Factor the trinomial completely.
- $81 y ^ { 2 } + 18 x y + x ^ { 2 }$

Accepted Answer

A)  $( x + 9 y ) ( x - 9 y )$ 
B)  $( x - 9 y ) ^ { 2 }$ 
C)  $( x + 9 y ) ^ { 2 }$ 
D) prime 
A)  $( x + 9 y ) ( x - 9 y )$ 
B)  $( x - 9 y ) ^ { 2 }$ 
C)  $( x + 9 y ) ^ { 2 }$ 
D) prime

Question 9

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-  $4 y ^ { 3 } - 8 y ^ { 2 } - 60 y$

Accepted Answer

A) 4y(y + 3)(y - 5) 
B) 4y(y - 3)(y + 5) 
C)  $( y - 3 ) \left( 4 y ^ { 2 } + 20 \right)$ 
D)  $\left( 4 y ^ { 2 } + 12 y \right) ( y - 5 )$ 
A) 4y(y + 3)(y - 5) 
B) 4y(y - 3)(y + 5) 
C)  $( y - 3 ) \left( 4 y ^ { 2 } + 20 \right)$ 
D)  $\left( 4 y ^ { 2 } + 12 y \right) ( y - 5 )$

Question 10

Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$2 a ^ { 2 } + 2 a b - 9 a - 9 b$

Accepted Answer

A) (2a - 9)(a - b) 
B) (2a + 9)(a - b) 
C) (2a - 9)(a + b) 
D) (2a + 9)(a + b) 
A) (2a - 9)(a - b) 
B) (2a + 9)(a - b) 
C) (2a - 9)(a + b) 
D) (2a + 9)(a + b)

Question 11

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$x ^ { 2 } - x - 63$

Accepted Answer

A) (x - 63)(x + 1) 
B) (x - 7)(x + 9) 
C) (x + 7)(x - 9) 
D) prime 
A) (x - 63)(x + 1) 
B) (x - 7)(x + 9) 
C) (x + 7)(x - 9) 
D) prime

Question 12

Factor the trinomial completely.
-$8 x ^ { 3 } - 22 x ^ { 2 } + 15 x$

Accepted Answer

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

Question 13

Complete the factored form.
-$7 x ^ { 2 } + 23 x - 20 = ( 7 x - 5 )$

Accepted Answer

A) (7x + 5) 
B) (x + 4) 
C) (x - 4) 
D) (7x - 4) 
A) (7x + 5) 
B) (x + 4) 
C) (x - 4) 
D) (7x - 4)

Question 14

Factor out the GCF from the polynomial.
-14p + 7q - 7

Accepted Answer

A) 7(2p + q) 
B) 7p(2 + q - 1) 
C) No common factor 
D) 7(2p + q - 1) 
A) 7(2p + q) 
B) 7p(2 + q - 1) 
C) No common factor 
D) 7(2p + q - 1)

Question 15

Factor the trinomial completely.
-$5 x ^ { 4 } + 13 x ^ { 2 } - 6$

Accepted Answer

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

Question 16

Factor the polynomial by grouping.
-$6 x ^ { 3 } - 22 x ^ { 2 } + 20 x$

Accepted Answer

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

Question 17

Factor the trinomial completely.
-  $10 x ^ { 2 } + 7 x y - 12 y ^ { 2 }$

Accepted Answer

A) (10x + 3y)(x - 4y) 
B) (2x - 3y)(5x + 4y) 
C) (2x + 3y)(5x - 4y) 
D) prime 
A) (10x + 3y)(x - 4y) 
B) (2x - 3y)(5x + 4y) 
C) (2x + 3y)(5x - 4y) 
D) prime

Question 18

Solve the equation.
-$\left( x + \frac { 1 } { 3 } \right) \left( x - \frac { 2 } { 5 } \right) = 0$

Accepted Answer

A)  $- \frac { 1 } { 3 } , \frac { 2 } { 5 }$ 
B) 2, 3 
C)  $3 , \frac { 5 } { 2 }$ 
D)  $\frac { 1 } { 3 } , - \frac { 2 } { 5 }$ 
A)  $- \frac { 1 } { 3 } , \frac { 2 } { 5 }$ 
B) 2, 3 
C)  $3 , \frac { 5 } { 2 }$ 
D)  $\frac { 1 } { 3 } , - \frac { 2 } { 5 }$

Question 19

Solve the equation.
-(x - 6)(x + 7)= 0

Accepted Answer

A) 6, -6, 7, -7 
B) 6, 7 
C) -6, 7 
D) 6, -7 
A) 6, -6, 7, -7 
B) 6, 7 
C) -6, 7 
D) 6, -7

Question 20

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

Accepted Answer

A) (2x - 4)(2x - 1) 
B) (4x - 1)(x - 4) 
C) (4x - 4)(x - 1) 
D) prime 
A) (2x - 4)(2x - 1) 
B) (4x - 1)(x - 4) 
C) (4x - 4)(x - 1) 
D) prime

Factor the trinomial completely. - $25 x ^ { 2 } y ^ { 2 } - 60 x ^ { 2 } y + 36 x ^ { 2 }$

Factor the four-term polynomial by grouping. -xy + 12x - 4y - 48

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $x ^ { 2 } - 4 x - 32$

Factor the trinomial completely. - $4 x ^ { 3 } y + 36 x ^ { 2 } y ^ { 2 } + 81 x y ^ { 3 }$

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $y ^ { 2 } + 50 y + 625$

Solve the equation. -(7y + 9)(2y + 29)= 0

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $- x ^ { 2 } - 3 x + 40$

Factor the trinomial completely. - $81 y ^ { 2 } + 18 x y + x ^ { 2 }$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $4 y ^ { 3 } - 8 y ^ { 2 } - 60 y$

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $2 a ^ { 2 } + 2 a b - 9 a - 9 b$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $x ^ { 2 } - x - 63$

Factor the trinomial completely. - $8 x ^ { 3 } - 22 x ^ { 2 } + 15 x$

Complete the factored form. - $7 x ^ { 2 } + 23 x - 20 = ( 7 x - 5 )$

Factor out the GCF from the polynomial. -14p + 7q - 7

Factor the trinomial completely. - $5 x ^ { 4 } + 13 x ^ { 2 } - 6$

Factor the polynomial by grouping. - $6 x ^ { 3 } - 22 x ^ { 2 } + 20 x$

Factor the trinomial completely. - $10 x ^ { 2 } + 7 x y - 12 y ^ { 2 }$

Solve the equation. - $\left( x + \frac { 1 } { 3 } \right) \left( x - \frac { 2 } { 5 } \right) = 0$

Solve the equation. -(x - 6)(x + 7)= 0

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

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Exam 13: Factoring Polynomials

Factor the trinomial completely. - 25x2y2−60x2y+36x225 x ^ { 2 } y ^ { 2 } - 60 x ^ { 2 } y + 36 x ^ { 2 }25x2y2−60x2y+36x2