Deck 6: Factoring Polynomials

Question 1

Factor out the GCF from the polynomial.
$$17 x ^ { 4 } - 11$$

A) cannot be factored
B) $17 \left( x ^ { 4 } - 11 \right)$
C) $17 \left( x ^ { 4 } - 187 \right)$
D) $17 \left( x ^ { 4 } - \frac { 11 } { 17 } \right)$

Answer 1

cannot be factored

Question 2

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

A) $704 x ^ { 8 } y ^ { 8 }$
B) $8 x ^ { 8 } y ^ { 8 }$
C) $4 x ^ { 3 } y ^ { 4 }$
D) $8 x ^ { 5 } y ^ { 4 }$

Answer 2

$8 x ^ { 5 } y ^ { 4 }$

Question 3

Find the greatest common factor of the monomials.
$16 x ^ { 10 }$ and $20 x ^ { 6 }$

A) $4 x ^ { 6 }$
B) $20 x ^ { 4 }$
C) $16 x ^ { 6 }$
D) $4 \mathrm { x } ^ { 10 }$

Answer 3

$4 x ^ { 6 }$

Question 4

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

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 5

Factor out the GCF from the polynomial.
$20 \mathrm { x } + 10$

A) $10 ( 2 x )$
B) $10 ( 2 x + 1 )$
C) $5 ( 4 x + 2 )$
D) $2 ( 10 x + 5 )$

Question 6

Find the greatest common factor of the monomials.
$- 6 x ^ { 10 }$ and $8 x ^ { 7 }$

A) $- 8 x ^ { 3 }$
B) $2 x ^ { 7 }$
C) $2 x ^ { 10 }$
D) $- 6 x ^ { 7 }$

Question 7

Find the greatest common factor of the monomials.
10xy, 10x², 12xy², and 6y²

A) 4
B) 2x
C) 2
D) 2xy

Question 8

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

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

Question 9

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

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

Question 10

Factor out the GCF from the polynomial.
$18 \mathrm { p } + 9 \mathrm { q } - 9$

A) $9 p ( 2 + q - 1 )$
B) cannot be factored
C) $9 ( 2 p + q - 1 )$
D) $9 ( 2 p + q )$

Question 11

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

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 12

Find the greatest common factor of the monomials.
$14 y ^ { 4 }$ and $56 y ^ { 7 }$

A) $14 \mathrm { y } ^ { 4 }$
B) $14 y ^ { 3 }$
C) $56 \mathrm { y } ^ { 4 }$
D) $784 \mathrm { y } ^ { 3 }$

Question 13

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

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 14

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

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

Question 15

Factor out the GCF from the polynomial.
$$8 x + 8$$

A) $8 x + 1$
B) $8 ( x + 8 )$
C) $8 ( x + 1 )$
D) $64 x$

Question 16

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

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

Question 17

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

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 18

Factor out the GCF from the polynomial.
$$3 x ^ { 6 } y + 12 x ^ { 4 }$$

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

Question 19

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

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 20

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

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 21

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

A) $x ^ { 3 } + 3 x ^ { 2 }$
B) $x + 9 x ^ { 2 }$
C) $x + 3$
D) $3 x ^ { 3 } + 6 x ^ { 2 }$

Question 22

Factor out the GCF from the polynomial.
$8 m ^ { 9 } - 18 m ^ { 5 } + 10 m ^ { 2 }$

A) $2 \left( 4 m ^ { 9 } - 9 m ^ { 5 } + 5 m ^ { 2 } \right)$
B) $- 2 m ^ { 2 } \left( 4 m ^ { 7 } + 9 m ^ { 3 } - 5 \right)$
C) $m ^ { 2 } \left( 8 m ^ { 7 } - 18 m ^ { 3 } + 10 \right)$
D) $2 m ^ { 2 } \left( 4 m ^ { 7 } - 9 m ^ { 3 } + 5 \right)$

Question 23

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

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 24

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

A) $( y - 8 ) ( x + 4 )$
B) $4 x ( y - 8 )$
C) $( x y - 8 x ) ( 4 y - 32 )$
D) $( y - 8 ) ( x - 4 )$

Question 25

Factor out the GCF from the polynomial.
$64 x ^ { 8 } y ^ { 9 } - 40 x ^ { 2 } y ^ { 7 } + 64 x ^ { 6 } y ^ { 3 }$

A) $x ^ { 2 } y ^ { 3 } \left( 64 x ^ { 6 } y ^ { 6 } - 40 y ^ { 4 } + 64 x ^ { 4 } \right)$
B) $8 x ^ { 2 } \left( 8 x ^ { 6 } y ^ { 9 } - 5 y ^ { 7 } + 8 x ^ { 4 } y ^ { 3 } \right)$
C) $8 \left( 8 x ^ { 8 } y ^ { 9 } - 5 x ^ { 2 } y ^ { 7 } + 8 x ^ { 6 } y ^ { 3 } \right)$
D) $8 x ^ { 2 } y ^ { 3 } \left( 8 x ^ { 6 } y ^ { 6 } - 5 y ^ { 4 } + 8 x ^ { 4 } \right)$

Question 26

Factor out the GCF from the polynomial.
$18 x ^ { 9 } y ^ { 9 } + 63 x ^ { 7 } y ^ { 7 } + 54 x ^ { 5 } y ^ { 5 }$

A) $9 x ^ { 5 } y ^ { 5 } \left( 2 x ^ { 4 } y ^ { 4 } + 7 x ^ { 2 } y ^ { 2 } + 6 \right)$
B) $9 \left( 2 x ^ { 9 } y ^ { 9 } + 7 x ^ { 7 } y ^ { 7 } + 6 x ^ { 5 } y ^ { 5 } \right)$
C) $- 9 x ^ { 5 } y ^ { 5 } \left( - 2 x ^ { 4 } y ^ { 4 } + 7 x ^ { 2 } y ^ { 2 } - 6 \right)$
D) $9 x ^ { 5 } \left( 2 x ^ { 4 } y ^ { 9 } + 7 x ^ { 2 } y ^ { 7 } + 6 y ^ { 5 } \right)$

Question 27

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

A) $4 a b \left( - 7 a b ^ { 2 } + 3 \right)$
B) $- 4 a \left( 7 a b ^ { 3 } - 3 b \right)$
C) $- 4 a b \left( 7 a b ^ { 2 } - 3 \right)$
D) $- 4 a b \left( 7 a b ^ { 2 } + 3 \right)$

Question 28

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

A) $\left( x ^ { 2 } - 5 x \right) ( 11 x - 55 )$
B) $( x + 5 ) ( x - 11 )$
C) $( x - 5 ) ( x - 11 )$
D) $( x - 5 ) ( x + 11 )$

Question 29

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

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 30

Factor the polynomial using the greatest common binomial factor.
$x ( x + 3 ) + 6 ( x + 3 )$

A) $\left( x ^ { 2 } + 3 x \right) ( 6 x + 18 )$
B) $( x - 3 ) ( x - 6 )$
C) $( x + 3 ) ( x + 6 )$
D) $\left( x ^ { 2 } + 3 \right) \left( x ^ { 2 } + 6 \right)$

Question 31

Factor out the GCF from the polynomial.
$60 x ^ { 9 } y ^ { 8 } + 72 x ^ { 6 } y ^ { 5 } - 60 x ^ { 2 } y ^ { 3 }$

A) $12 x ^ { 2 } y ^ { 3 } \left( 5 x ^ { 7 } y ^ { 5 } + 6 x ^ { 4 } y ^ { 2 } - 5 \right)$
B) $12 \left( 5 x ^ { 9 } y ^ { 8 } + 6 x ^ { 6 } y ^ { 5 } - 5 x ^ { 2 } y ^ { 3 } \right)$
C) $12 x ^ { 2 } \left( 5 x ^ { 7 } y ^ { 8 } + 6 x ^ { 4 } y ^ { 5 } - 5 y ^ { 3 } \right)$
D) cannot be factored

Question 32

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) $18 x + 18 x ^ { 5 }$

Question 33

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

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

Question 34

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

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 35

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

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 36

Factor the polynomial using the greatest common binomial factor.
$$x ( x + 13 ) - 3 ( x + 13 )$$

A) $( x + 13 ) ( x + 3 )$
B) $( x - 13 ) ( x + 3 )$
C) $\left( x ^ { 2 } + 13 x \right) ( 3 x + 39 )$
D) $( x + 13 ) ( x - 3 )$

Question 37

Factor the polynomial using the negative of the greatest common factor.
$$- 27 x ^ { 3 } y ^ { 2 } + 6 x ^ { 3 } y - 12 x ^ { 2 } y$$

A) $- 3 x ^ { 2 } y ( 9 x y + 2 x - 4 )$
B) $- 3 x y \left( 9 x ^ { 2 } y - 2 x ^ { 2 } + 4 x \right)$
C) $3 x ^ { 2 } y ( - 9 x y + 2 x - 4 )$
D) $- 3 x ^ { 2 } y ( 9 x y - 2 x + 4 )$

Question 38

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

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

Question 39

Factor the polynomial using the negative of the greatest common factor.
$$- 24 x ^ { 2 } + 16$$

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

Question 40

Factor the polynomial using the negative of the greatest common factor.
$- 10 x ^ { 2 } - 6$

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

Question 41

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

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 42

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

A) $x ^ { 2 } ( x - 7 )$
B) $( x - 7 ) \left( x ^ { 2 } + 1 \right)$
C) $\left( x ^ { 3 } - 7 x ^ { 2 } \right) - ( x - 7 )$
D) $( x - 7 ) \left( x ^ { 2 } - 2 \right)$

Question 43

Factor completely.
$$x ^ { 2 } - x - 6$$

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

Question 44

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

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 45

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

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

Question 46

Factor the polynomial using the greatest common binomial factor.
$8 x ^ { 2 } ( 8 x - 5 ) + 8 x - 5$

A) $9 x ^ { 2 } ( 8 x - 5 )$
B) $2 ( 8 x - 5 ) \left( 8 x ^ { 2 } \right)$
C) $9 x ^ { 2 } \left( 8 x ^ { 2 } + 1 \right)$
D) $( 8 x - 5 ) \left( 8 x ^ { 2 } + 1 \right)$

Question 47

Factor by grouping.
$$3 x ^ { 2 } + 9 x y - 4 x y - 12 y ^ { 2 }$$

A) $( 3 x + 4 y ) ( x + 3 y )$
B) $\left( 3 x ^ { 2 } - 4 y \right) ( 1 + 3 y )$
C) $( 3 x - 4 y ) ( x - 3 y )$
D) $( 3 x - 4 y ) ( x + 3 y )$

Question 48

Write a polynomial for the length of the rectangle.

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

Question 49

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

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 50

Factor completely.
$$x ^ { 2 } + 5 x - 14$$

A) $( x - 7 ) ( x + 1 )$
B) prime
C) $( x - 7 ) ( x + 2 )$
D) $( x + 7 ) ( x - 2 )$

Question 51

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

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

Question 52

Write a polynomial for the length of the rectangle.

A) $x ^ { 2 } + 8$
B) $x - 5$
C) $x ^ { 2 } - 6 x - 8 x + 35$
D) $x + 40$

Question 53

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

A) $( 14 y + 140 ) - ( x y + 10 x )$
B) $( y + 10 ) ( 14 + x )$
C) $( \mathrm { y } + 10 ) ( 14 - \mathrm { x } )$
D) $( \mathrm { y } - 10 ) ( \mathrm { x } - 14 )$

Question 54

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

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 55

Factor completely.
x² - 10x + 24

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

Question 56

Factor completely.
x² - x - 45

A) (x + 5)(x - 9)
B) prime
C) (x - 5)(x + 9)
D) (x - 45)(x + 1)

Question 57

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

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 58

Factor by grouping.
$x ^ { 2 } - 4 x - 3 x + 12$

A) $( x - 3 ) ( x + 8 )$
B) $( x + 3 ) ( x - 4 )$
C) $- 7 x \left( x ^ { 2 } + 12 \right)$
D) $( x - 3 ) ( x - 4 )$

Question 59

Factor by grouping.
$10 x ^ { 6 } - 25 x ^ { 3 } + 8 x ^ { 3 } - 20$

A) $\left( 5 x ^ { 6 } + 4 \right) ( 2 x - 5 )$
B) $\left( 10 x ^ { 3 } - 4 \right) \left( x ^ { 3 } + 5 \right)$
C) $\left( 5 x ^ { 3 } + 4 \right) \left( 2 x ^ { 3 } - 5 \right)$
D) $\left( 5 x ^ { 3 } - 4 \right) \left( 2 x ^ { 3 } + 5 \right)$

Question 60

Factor by grouping.
$10 x ^ { 10 } - 15 x ^ { 5 } y ^ { 4 } + 6 x ^ { 5 } y ^ { 4 } - 9 y ^ { 8 }$

A) $\left( 5 x ^ { 5 } + 3 y \right) \left( 2 x ^ { 5 } - 3 y ^ { 8 } \right)$
B) $\left( 5 x ^ { 5 } + 3 y ^ { 4 } \right) \left( 2 x ^ { 5 } - 3 y ^ { 4 } \right)$
C) $\left( 10 x ^ { 5 } + 3 y ^ { 4 } \right) \left( x ^ { 5 } - 3 y ^ { 4 } \right)$
D) $\left( 5 x ^ { 5 } - 3 y ^ { 4 } \right) \left( 2 x ^ { 5 } + 3 y ^ { 4 } \right)$

Question 61

Factor completely. If unfactorable, indicate that the polynomial is prime.
$$x ^ { 2 } - \frac { 2 } { 9 } x + \frac { 1 } { 81 }$$

A) $\left( x + \frac { 1 } { 9 } \right) \left( x - \frac { 1 } { 9 } \right)$
B) prime
C) $\left( x + \frac { 1 } { 9 } \right) \left( x + \frac { 1 } { 9 } \right)$
D) $\left( x - \frac { 1 } { 9 } \right) \left( x - \frac { 1 } { 9 } \right)$

Question 62

Factor completely.
x² + 4xy - 96y²

A) (x - 12y)(x + 8y)
B) prime
C) (x + 12y)(x - 8y)
D) (x - 12y)(x + y)

Question 63

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

A) $( 9 x + 2 ) ( x + 4 )$
B) prime
C) $( 3 x + 2 ) ( 3 x + 4 )$
D) $( 3 x - 2 ) ( 3 x - 4 )$

Question 64

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is
prime.
$$3 x ^ { 2 } + 34 x + 11$$

A) $( 3 x + 1 ) ( x + 11 )$
B) prime
C) $( 3 x - 1 ) ( x - 11 )$
D) $( 3 x + 11 ) ( x + 1 )$

Question 65

Factor completely.
5x6 + 40x5 - 45x4

A) 5x4(x - 1)(x + 9)
B) 5x⁴(x² + 8x - 9)
C) x4(5x - 5)(x + 9)
D) x4(x - 1)(5x + 45)

Question 66

Factor completely.
x²(y - 5) - 12x(y - 5) + 20(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 67

Factor completely.
x³y + 6x²y² + 8xy³

A) xy(x + 4y)(x + 2y)
B) y(x + 4y)(xy + 2y²)
C) x(xy + 4y²)(x + 2y)
D) xy(x² + 6x + 8y²)

Question 68

Factor completely.
u² - 4uv - 21v²

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

Question 69

Factor completely.
x²+ 12xy + 27y²

A) (x - 9y)(x + y)
B) (x + 9y)(x + 3y)
C) (x - 9y)(x + 3y)
D) prime

Question 70

Factor completely.
x² + 34x + 35

A) (x + 35)(x - 1)
B) (x - 7)(x + 5)
C) (x + 7)(x - 5)
D) prime

Question 71

Factor completely.
x5 + 4x4 - 45x3

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

Question 72

Factor completely.
5x²- 25x + 30

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

Question 73

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

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

Question 74

Factor completely. If unfactorable, indicate that the polynomial is prime.
$$- x ^ { 2 } + 6 x + 40$$

A) $( x - 4 ) ( x + 10 )$
B) prime
C) $- ( x + 4 ) ( x - 10 )$
D) $- ( x - 4 ) ( x + 10 )$

Question 75

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

A) (a + b)(x + 6)(x - 10)
B) prime
C) (ax + 6b)(ax - 10b)
D) (a +b)(x - 6)(x + 10)

Question 76

Factor completely.
x5 + 6x4 + 8x3

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

Question 77

Factor completely.
2x²- 2x - 12

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

Question 78

Factor completely.
x³ - x² - 12x

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

Question 79

Factor completely.
2x²- 6xy - 8y²

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

Question 80

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is
prime.
$$2 x ^ { 2 } + 6 x - 20$$

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