Question 1

Factor the four-term polynomial by grouping.
-$x ^ { 3 } + 4 x + x ^ { 2 } + 4$

Accepted Answer

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

Question 2

Determine whether the trinomial is a perfect square trinomial.
-$25 x ^ { 2 } - 50 x y + 25 y ^ { 2 }$

Accepted Answer

A) True 
 B)False

Question 3

Factor the four-term polynomial by grouping.
-$10 x ^ { 2 } + 12 x y + 15 x y + 18 y ^ { 2 }$

Accepted Answer

A) (10x + 3y)(x + 6y) 
B) (2x + 3)(5x + 6) 
C) (2x + 3y)(5x + 6y) 
D) (2x - 3y)(5x + 6y) 
A) (10x + 3y)(x + 6y) 
B) (2x + 3)(5x + 6) 
C) (2x + 3y)(5x + 6y) 
D) (2x - 3y)(5x + 6y)

Question 4

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$8 y ^ { 4 } + 64 y ^ { 3 } + 120 y ^ { 2 }$

Accepted Answer

A)  $8 y \left( y ^ { 2 } + 5 y \right) ( y + 3 )$ 
B)  $8 \left( y ^ { 2 } + 5 \right) \left( y ^ { 2 } + 3 \right)$ 
C)  $y ^ { 2 } ( y + 5 ) ( 8 y + 24 )$ 
D)  $8 y ^ { 2 } ( y + 5 ) ( y + 3 )$ 
A)  $8 y \left( y ^ { 2 } + 5 y \right) ( y + 3 )$ 
B)  $8 \left( y ^ { 2 } + 5 \right) \left( y ^ { 2 } + 3 \right)$ 
C)  $y ^ { 2 } ( y + 5 ) ( 8 y + 24 )$ 
D)  $8 y ^ { 2 } ( y + 5 ) ( y + 3 )$

Question 5

Factor the polynomial by grouping.
-$3 x ^ { 4 } - 8 x ^ { 2 } + 9 x ^ { 2 } - 24$

Accepted Answer

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

Question 6

Find the GCF for the list.
-$64 a ^ { 9 } b ^ { 2 } , 88 a ^ { 5 } b ^ { 9 }$

Accepted Answer

A)  $4 a ^ { 4 } b ^ { 7 }$ 
B)  $8 a ^ { 5 } b ^ { 2 }$ 
C)  $704 a ^ { 9 } b ^ { 9 }$ 
D)  $8 a ^ { 9 } b ^ { 9 }$ 
A)  $4 a ^ { 4 } b ^ { 7 }$ 
B)  $8 a ^ { 5 } b ^ { 2 }$ 
C)  $704 a ^ { 9 } b ^ { 9 }$ 
D)  $8 a ^ { 9 } b ^ { 9 }$

Question 7

Determine whether the trinomial is a perfect square trinomial.
-x $x ^ { 2 } + 4 x + 4$

Accepted Answer

A) True 
 B)False

Question 8

Factor the binomial completely.
-$4 - 49 x ^ { 2 }$

Accepted Answer

A) (2 + 7x)(2 - 7x) 
B)  $( 2 + 7 x ) ^ { 2 }$ 
C)  $( 2 - 7 x ) ^ { 2 }$ 
D) prime 
A) (2 + 7x)(2 - 7x) 
B)  $( 2 + 7 x ) ^ { 2 }$ 
C)  $( 2 - 7 x ) ^ { 2 }$ 
D) prime

Question 9

Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$625 x - x ^ { 5 }$

Accepted Answer

A)  $x \left( x ^ { 2 } + 25 \right) ^ { 2 }$ 
B)  $x \left( x ^ { 2 } - 25 \right) ^ { 2 }$ 
C)  $x \left( 25 + x ^ { 2 } \right) ( 5 - x ) ( 5 + x )$ 
D) prime 
A)  $x \left( x ^ { 2 } + 25 \right) ^ { 2 }$ 
B)  $x \left( x ^ { 2 } - 25 \right) ^ { 2 }$ 
C)  $x \left( 25 + x ^ { 2 } \right) ( 5 - x ) ( 5 + x )$ 
D) prime

Question 10

Factor the polynomial by grouping.
-$20 + 63 x ^ { 2 } - 73 x$

Accepted Answer

A) (9x + 4)(-7x + 5) 
B) (9x - 4)(7x - 5) 
C) (9x - 4)(7x + 5) 
D) prime 
A) (9x + 4)(-7x + 5) 
B) (9x - 4)(7x - 5) 
C) (9x - 4)(7x + 5) 
D) prime

Question 11

Factor the trinomial completely.
-$- 3 x ^ { 2 } + 11 x - 10$

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

Represent the given condition using a single variable, x.
-The length and width of a rectangle whose width is nine times its length.

Accepted Answer

A) length = x; width = 9x 
B) width = x; length = 9x 
C) width = x; length = x + 9 
D) length = x; width = x + 9 
A) length = x; width = 9x 
B) width = x; length = 9x 
C) width = x; length = x + 9 
D) length = x; width = x + 9

Question 14

Factor the polynomial by grouping.
-$2 x ^ { 2 } + 7 x + 14 x + 49$

Accepted Answer

A) (2x + 7)(2x + 7) 
B) (x + 7)(2x + 7) 
C) (2x + 7)(7x + 2) 
D) prime 
A) (2x + 7)(2x + 7) 
B) (x + 7)(2x + 7) 
C) (2x + 7)(7x + 2) 
D) prime

Question 15

Solve.
-The sum of two numbers is 11, and the sum of their squares is 65. Find the numbers.

Accepted Answer

A) 5 and 6 
B) 3 and 8 
C) 6 and 5 
D) 4 and 7 
A) 5 and 6 
B) 3 and 8 
C) 6 and 5 
D) 4 and 7

Question 16

Find the GCF for the list.
-$297 x ^ { 2 } , 99 x ^ { 9 }$

Accepted Answer

A)  $33 x ^ { 7 }$ 
B)  $99 x ^ { 7 }$ 
C)  $99 x ^ { 2 }$ 
D)  $297 x ^ { 2 }$ 
A)  $33 x ^ { 7 }$ 
B)  $99 x ^ { 7 }$ 
C)  $99 x ^ { 2 }$ 
D)  $297 x ^ { 2 }$

Question 17

Solve the equation.
-$x ^ { 2 } - 9 x = - 8$

Accepted Answer

A) 8, 1 
B) -1, 8 
C) -1, -8 
D) -8, 8 
A) 8, 1 
B) -1, 8 
C) -1, -8 
D) -8, 8

Question 18

Factor the binomial completely.
-$z ^ { 2 } - 64$

Accepted Answer

A)  $( x - 8 ) ^ { 2 }$ 
B) (z + 8)(z - 8) 
C)  $( x + 8 ) ^ { 2 }$ 
D) prime 
A)  $( x - 8 ) ^ { 2 }$ 
B) (z + 8)(z - 8) 
C)  $( x + 8 ) ^ { 2 }$ 
D) prime

Question 19

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$5 r ^ { 6 } - 15 r ^ { 5 } - 50 r ^ { 4 }$

Accepted Answer

A)  $5 r ^ { 4 } ( r - 2 ) ( r + 5 )$ 
B)  $\left( 5 r ^ { 3 } + 25 \right) ( r - 2 )$ 
C)  $\left( 5 r ^ { 3 } + 10 \right) ( r - 5 )$ 
D)  $5 r ^ { 4 } ( r + 2 ) ( r - 5 )$ 
A)  $5 r ^ { 4 } ( r - 2 ) ( r + 5 )$ 
B)  $\left( 5 r ^ { 3 } + 25 \right) ( r - 2 )$ 
C)  $\left( 5 r ^ { 3 } + 10 \right) ( r - 5 )$ 
D)  $5 r ^ { 4 } ( r + 2 ) ( r - 5 )$

Question 20

Solve the equation.
-$x ^ { 2 } + 3 x - 108 = 0$

Accepted Answer

A) 12, 9 
B) 12, -9 
C) -12, 9 
D) -12, 1 
A) 12, 9 
B) 12, -9 
C) -12, 9 
D) -12, 1

Factor the four-term polynomial by grouping. - $x ^ { 3 } + 4 x + x ^ { 2 } + 4$

Determine whether the trinomial is a perfect square trinomial. - $25 x ^ { 2 } - 50 x y + 25 y ^ { 2 }$

Factor the four-term polynomial by grouping. - $10 x ^ { 2 } + 12 x y + 15 x y + 18 y ^ { 2 }$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $8 y ^ { 4 } + 64 y ^ { 3 } + 120 y ^ { 2 }$

Factor the polynomial by grouping. - $3 x ^ { 4 } - 8 x ^ { 2 } + 9 x ^ { 2 } - 24$

Find the GCF for the list. - $64 a ^ { 9 } b ^ { 2 } , 88 a ^ { 5 } b ^ { 9 }$

Determine whether the trinomial is a perfect square trinomial. -x $x ^ { 2 } + 4 x + 4$

Factor the binomial completely. - $4 - 49 x ^ { 2 }$

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $625 x - x ^ { 5 }$

Factor the polynomial by grouping. - $20 + 63 x ^ { 2 } - 73 x$

Factor the trinomial completely. - $- 3 x ^ { 2 } + 11 x - 10$

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

Represent the given condition using a single variable, x. -The length and width of a rectangle whose width is nine times its length.

Factor the polynomial by grouping. - $2 x ^ { 2 } + 7 x + 14 x + 49$

Solve. -The sum of two numbers is 11, and the sum of their squares is 65. Find the numbers.

Find the GCF for the list. - $297 x ^ { 2 } , 99 x ^ { 9 }$

Solve the equation. - $x ^ { 2 } - 9 x = - 8$

Factor the binomial completely. - $z ^ { 2 } - 64$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $5 r ^ { 6 } - 15 r ^ { 5 } - 50 r ^ { 4 }$

Solve the equation. - $x ^ { 2 } + 3 x - 108 = 0$

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Exam 13: Factoring Polynomials

Factor the four-term polynomial by grouping. - x3+4x+x2+4x ^ { 3 } + 4 x + x ^ { 2 } + 4x3+4x+x2+4

Determine whether the trinomial is a perfect square trinomial. - 25x2−50xy+25y225 x ^ { 2 } - 50 x y + 25 y ^ { 2 }25x2−50xy+25y2

Factor the four-term polynomial by grouping. - 10x2+12xy+15xy+18y210 x ^ { 2 } + 12 x y + 15 x y + 18 y ^ { 2 }10x2+12xy+15xy+18y2

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - 8y4+64y3+120y28 y ^ { 4 } + 64 y ^ { 3 } + 120 y ^ { 2 }8y4+64y3+120y2

Factor the polynomial by grouping. - 3x4−8x2+9x2−243 x ^ { 4 } - 8 x ^ { 2 } + 9 x ^ { 2 } - 243x4−8x2+9x2−24

Find the GCF for the list. - 64a9b2,88a5b964 a ^ { 9 } b ^ { 2 } , 88 a ^ { 5 } b ^ { 9 }64a9b2,88a5b9

Determine whether the trinomial is a perfect square trinomial. -x x2+4x+4x ^ { 2 } + 4 x + 4x2+4x+4

Factor the binomial completely. - 4−49x24 - 49 x ^ { 2 }4−49x2

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - 625x−x5625 x - x ^ { 5 }625x−x5

Factor the polynomial by grouping. - 20+63x2−73x20 + 63 x ^ { 2 } - 73 x20+63x2−73x

Factor the trinomial completely. - −3x2+11x−10- 3 x ^ { 2 } + 11 x - 10−3x2+11x−10

Factor the four-term polynomial by grouping. -10 10x2−8x−15x+1210 x ^ { 2 } - 8 x - 15 x + 1210x2−8x−15x+12