Deck 6: Factoring

Question 1

Factor out the largest possible common factor.
$16 m ^ { 9 } - 16 m ^ { 4 } - 28 m ^ { 2 }$

A) $4 m ^ { 2 } \left( 4 m ^ { 7 } - 4 m ^ { 2 } - 7 \right)$
B) $m ^ { 2 } \left( 16 m ^ { 7 } - 16 m ^ { 2 } - 28 \right)$
C) $4 \left( 4 m ^ { 9 } - 4 m ^ { 4 } - 7 m ^ { 2 } \right)$
D) No common factor

Answer 1

A

Question 2

Factor out the largest possible common factor.
$3 x + 15 + x y + 5 y$

A) $( x + 5 y ) ( 3 + y )$
B) $( y + 5 ) ( x + 3 )$
C) $( x + 5 ) ( 3 + y )$
D) $( y + 5 ) ( 3 x + y )$

Answer 2

C

Question 3

Factor out the largest possible common factor.
$21 y ^ { 3 } - 6 y ^ { 2 } + 15 y$

A) $y \left( 21 y ^ { 2 } - 6 y + 15 \right)$
B) $3 y \left( 7 y ^ { 3 } - 2 y ^ { 2 } + 5 y \right)$
C) $3 y \left( 7 y ^ { 2 } - 2 y + 5 \right)$
D) $3 \left( 7 y ^ { 3 } - 2 y ^ { 2 } + 5 y \right)$

Answer 3

C

Question 4

Factor out the largest possible common factor.
$$m ^ { 2 } ( n - 4 ) - ( n - 4 )$$

A) $m ^ { 2 } ( n - 4 )$
B) $\left( m ^ { 2 } n - 4 m ^ { 2 } \right) - ( n - 4 )$
C) $( n - 4 ) \left( m ^ { 2 } + 1 \right)$
D) $( \mathrm { n } - 4 ) \left( \mathrm { m } ^ { 2 } - 1 \right)$

Question 5

Factor out the largest possible common factor.
$$3 ( y + 14 ) - x ( y + 14 )$$

A) $( y - 14 ) ( x - 3 )$
B) $( 3 y + 42 ) - ( x y + 14 x )$
C) $( y + 14 ) ( 3 + x )$
D) $( y + 14 ) ( 3 - x )$

Question 6

Factor out the largest possible common factor.
$$84 x ^ { 8 } y ^ { 9 } + 72 x ^ { 2 } y ^ { 7 } + 108 x ^ { 4 } y ^ { 2 }$$

A) $12 \left( 7 x ^ { 8 } y ^ { 9 } + 6 x ^ { 2 } y ^ { 7 } + 9 x ^ { 4 } y ^ { 2 } \right)$
B) $12 x ^ { 2 } y ^ { 2 } \left( 7 x ^ { 6 } y ^ { 7 } + 6 y ^ { 5 } + 9 x ^ { 2 } \right)$
C) $12 x ^ { 2 } \left( 7 x ^ { 6 } y ^ { 9 } + 6 y ^ { 7 } + 9 x ^ { 2 } y ^ { 2 } \right)$
D) $x ^ { 2 } y ^ { 2 } \left( 84 x ^ { 6 } y ^ { 7 } + 72 y ^ { 5 } + 108 x ^ { 2 } \right)$

Question 7

Factor out the largest possible common factor.
$$w ( z - 12 ) - 10 ( z - 12 )$$

A) $( w z - 12 w ) - ( 10 z - 120 )$
B) $( z - 12 ) ( w + 10 )$
C) $10 w ( z - 12 )$
D) $( z - 12 ) ( w - 10 )$

Question 8

Factor out the largest possible common factor.
$5 a ( a - b ) + ( a - b )$

A) $\left( 5 a ^ { 2 } + 5 b \right) + ( a - b )$
B) $5 a ( a - b )$
C) $6 a ( a - b )$
D) $( a - b ) ( 5 a + 1 )$

Question 9

Factor out the largest possible common factor.
$$x y + y + 6 x + 6$$

A) $( x + 6 ) ( y + 1 )$
B) $( x + 1 ) ( y + 6 )$
C) $( x + 1 ) ( 6 y + 6 )$
D) $( 6 x + 6 ) ( y + 1 )$

Question 10

Factor out the largest possible common factor.
$$x y + 11 x - 8 y - 88$$

A) $( x - 11 ) ( y + 8 )$
B) $( y - 11 ) ( x + 8 )$
C) $( y + 11 ) ( x - 8 )$
D) $( x + 11 ) ( y - 8 )$

Question 11

Factor out the largest possible common factor.
$48 x ^ { 9 } y ^ { 9 } + 24 x ^ { 7 } y ^ { 4 } - 60 x ^ { 5 } y ^ { 2 }$

A) $12 \left( 4 x ^ { 9 } y ^ { 9 } + 2 x ^ { 7 } y ^ { 4 } - 5 x ^ { 5 } y ^ { 2 } \right)$
B) No common factor
C) $12 x ^ { 5 } y ^ { 2 } \left( 4 x ^ { 4 } y ^ { 7 } + 2 x ^ { 2 } y ^ { 2 } - 5 \right)$
D) $12 x ^ { 5 } \left( 4 x ^ { 4 } y ^ { 9 } + 2 x ^ { 2 } y ^ { 4 } - 5 y ^ { 2 } \right)$

Question 12

Factor out the largest possible common factor.
$$60 \mathrm { x } + 20$$

A) $20 ( 3 x + 1 )$
B) $20 ( 3 x )$
C) $4 ( 15 x + 5 )$
D) $5 ( 12 x + 4 )$

Question 13

Factor out the largest possible common factor.
$32 \mathrm { p } + 8 \mathrm { q } - 8$

A) $8 ( 4 p + q )$
B) $8 \mathrm { p } ( 4 + \mathrm { q } - 1 )$
C) $8 ( 4 p + q - 1 )$
D) No common factor

Question 14

Factor out the largest possible common factor.
$42 m ^ { 6 } - 12 m ^ { 4 } - 30 m ^ { 2 }$

A) $6 m ^ { 2 } \left( 7 m ^ { 4 } - 2 m ^ { 2 } - 5 \right)$
B) $- m ^ { 2 } \left( - 42 m ^ { 4 } - 12 m ^ { 2 } + 30 \right)$
C) $m ^ { 2 } \left( 42 m ^ { 4 } - 12 m ^ { 2 } - 30 \right)$
D) $6 \left( 7 m ^ { 6 } - 2 m ^ { 4 } - 5 m ^ { 2 } \right)$

Question 15

Factor out the largest possible common factor.
$20 x ^ { 8 } y ^ { 9 } - 40 x ^ { 6 } y ^ { 7 } - 28 x ^ { 4 } y ^ { 5 }$

A) $4 x ^ { 4 } y ^ { 5 } \left( 5 x ^ { 4 } y ^ { 4 } - 10 x ^ { 2 } y ^ { 2 } - 7 \right)$
B) $4 \left( 5 x ^ { 8 } y ^ { 9 } - 10 x ^ { 6 } y ^ { 7 } - 7 x ^ { 4 } y ^ { 5 } \right)$
C) $- 4 x ^ { 4 } y ^ { 5 } \left( - 5 x ^ { 4 } y ^ { 4 } - 10 x ^ { 2 } y ^ { 2 } + 7 \right)$
D) $4 x ^ { 4 } \left( 5 x ^ { 4 } y ^ { 9 } - 10 x ^ { 2 } y ^ { 7 } - 7 y ^ { 5 } \right)$

Question 16

Factor out the largest possible common factor.
$28 m ^ { 7 } + 16 m ^ { 5 } - 32 m ^ { 3 }$

A) $4 \left( 7 m ^ { 7 } + 4 m ^ { 5 } - 8 m ^ { 3 } \right)$
B) $4 m ^ { 3 } \left( 7 m ^ { 4 } + 4 m ^ { 2 } - 8 \right)$
C) $m ^ { 3 } \left( 28 m ^ { 4 } + 16 m ^ { 2 } - 32 \right)$
D) $- 4 m ^ { 3 } \left( 7 m ^ { 4 } - 4 m ^ { 2 } + 8 \right)$

Question 17

Factor out the largest possible common factor.
$$16 x ^ { 4 } y + 14 x y ^ { 6 }$$

A) $2 y \left( 8 x ^ { 4 } + 7 x y ^ { 5 } \right)$
B) $2 x \left( 8 x ^ { 3 } y + 7 y ^ { 6 } \right)$
C) $2 x y \left( 8 x ^ { 3 } + 7 y ^ { 5 } \right)$
D) $x y \left( 16 x ^ { 3 } + 14 y ^ { 5 } \right)$

Question 18

Factor out the largest possible common factor.
$$x ( y + 12 ) + 4 ( y + 12 )$$

A) $4 x ( y + 12 )$
B) $( y + 12 ) ( x + 4 )$
C) $12 y ( x + 4 )$
D) $( x y + 12 x ) + ( 4 y + 48 )$

Question 19

Factor out the largest possible common factor.
$$p q ( p - 13 ) + ( p - 13 )$$

A) $p q ( p - 13 )$
B) $( \mathrm { p } - 13 ) ( \mathrm { pq } + 1 )$
C) $( p - 13 ) ( p q - 1 )$
D) $\left( p ^ { 2 } q - 13 p q \right) + ( p - 13 )$

Question 20

Factor out the largest possible common factor.
$$s \left( t ^ { 2 } - 7 \right) + 15 \left( t ^ { 2 } - 7 \right)$$

A) $\left( \mathrm { t } ^ { 2 } - 7 \right) ( \mathrm { s } - 15 )$
B) $15 s \left( t ^ { 2 } - 7 \right)$
C) $\left( s ^ { 2 } - 7 s \right) + \left( 15 t ^ { 2 } - 105 \right)$
D) $\left( t ^ { 2 } - 7 \right) ( s + 15 )$

Question 21

Factor.
$$3 x ^ { 2 } - 18 x + 27$$

A) $3 ( x - 3 ) ( x - 3 )$
B) $( x - 3 ) ( 3 x - 9 )$
C) $3 ( x - 9 ) ( x + 1 )$
D) $3 x ^ { 2 } - 18 x + 27$

Question 22

Factor.
$$9 x ^ { 2 } - 9 x - 54$$

A) $9 x ^ { 2 } - 9 x - 54$
B) $( 9 x + 18 ) ( x - 3 )$
C) $9 ( x + 2 ) ( x - 3 )$
D) $9 ( x - 2 ) ( x + 3 )$

Question 23

Factor out the largest possible common factor.
$5 x - 55 + x y - 11 y$

A) $( x - 11 y ) ( 5 + y )$
В) $( x - 11 ) ( 5 + y )$
C) $( y - 11 ) ( 5 x + y )$
D) $( y - 11 ) ( x + 5 )$

Question 24

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

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

Question 25

Factor out the largest possible common factor.
$12 x ^ { 2 } + 20 x y - 15 x y - 25 y ^ { 2 }$

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

Question 26

Factor out the largest possible common factor.
$$8 x ^ { 2 } - 6 x + 20 x - 15$$

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

Question 27

Factor out the largest possible common factor.
$20 x ^ { 2 } - 25 x - 16 x + 20$

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

Question 28

Factor out the largest possible common factor.
$$6 x ^ { 6 } - 8 x ^ { 3 } - 15 x ^ { 3 } + 20$$

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

Question 29

Factor out the largest possible common factor.
$$15 a ^ { 3 } - 6 a ^ { 2 } b - 25 a b ^ { 2 } + 10 b ^ { 3 }$$

A) $\left( 3 a ^ { 2 } - 5 b \right) ( 5 a - 2 b )$
B) $\left( 3 a ^ { 2 } - 5 b ^ { 2 } \right) ( 5 a - 2 b )$
C) $\left( 3 a ^ { 2 } + 5 b ^ { 2 } \right) ( 5 a + 2 b )$
D) $\left( 15 a ^ { 2 } - 5 b ^ { 2 } \right) ( a - 2 b )$

Question 30

Factor.
$5 x ^ { 4 } - 50 x ^ { 3 } + 105 x ^ { 2 }$

A) $x ^ { 2 } ( 5 x - 15 ) ( x - 7 )$
B) $5 x ^ { 2 } \left( x ^ { 2 } - 10 x + 21 \right)$
C) $x ^ { 2 } ( x - 3 ) ( 5 x - 35 )$
D) $5 x ^ { 2 } ( x - 3 ) ( x - 7$

Question 31

Factor.
$$x ^ { 2 } + 10 x + 9$$

A) $( x - 1 ) ( x - 9 )$
B) $( x + 1 ) ( x - 9 )$
C) $( x - 1 ) ( x + 9 )$
D) $( x + 1 ) ( x + 9 )$

Question 32

Factor out the largest possible common factor.
$$8 a ^ { 3 } + 6 a ^ { 2 } b - 20 a b ^ { 2 } - 15 b ^ { 3 }$$

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

Question 33

Factor out the largest possible common factor.
$18 x ^ { 2 } + 24 x y + 15 x y + 20 y ^ { 2 }$

A) $( 6 x + 5 ) ( 3 x + 4 )$
B) $( 6 x + 5 y ) ( 3 x + 4 y )$
C) $( 18 x + 5 y ) ( x + 4 y )$
D) $( 6 x - 5 y ) ( 3 x + 4 y )$

Question 34

Factor out the largest possible common factor.
$7 y - 63 + x y - 9 x$

A) $( y - 9 x ) ( 7 + x )$
В) $( x - 9 ) ( y + 7 )$
C) $( y - 9 ) ( 7 + x )$
D) $( x - 9 ) ( 7 y + x )$

Question 35

Factor out the largest possible common factor.
$$x ^ { 3 } + 6 x ^ { 2 } + x + 6$$

A) $\left( 6 x ^ { 2 } + 6 \right) ( x + 1 )$
B) $\left( x ^ { 2 } + 1 \right) ( 6 x + 6 )$
C) $\left( x ^ { 2 } + 6 \right) ( x + 1 )$
D) $\left( x ^ { 2 } + 1 \right) ( x + 6 )$

Question 36

Factor.
$$x ^ { 2 } + 7 x - 44$$

A) $x ^ { 2 } + 7 x - 44$
B) $( x - 11 ) ( x + 1 )$
C) $( x - 11 ) ( x + 4 )$
D) $( x + 11 ) ( x - 4 )$

Question 37

Factor.
$$x ^ { 3 } - x ^ { 2 } - 42 x$$

A) $x ( x + 7 ) ( x - 6 )$
B) $x ( x + 6 ) ( x - 7 )$
C) $\left( x ^ { 2 } + 1 \right) ( x - 42 )$
D) $x ^ { 3 } - x ^ { 2 } - 42$

Question 38

Factor.
$$x ^ { 2 } - x - 30$$

A) $( x + 5 ) ( x - 6 )$
B) $( x + 1 ) ( x - 30 )$
C) $( x + 6 ) ( x - 5 )$
D) $x ^ { 2 } - x - 30$

Question 39

Factor.
$$x ^ { 2 } + 4 x - 5$$

A) $( x - 1 ) ( x + 5 )$
B) $( x + 1 ) ( x + 1 )$
C) $( x + 1 ) ( x + 5 )$
D) $x ^ { 2 } + 4 x - 5$

Question 40

Factor.
$$x ^ { 2 } - 11 x + 28$$

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

Question 41

Factor using the trial and error method
$4 x ^ { 2 } - x - 3$

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

Question 42

Factor using the trial and error method
$20 y ^ { 2 } - 27 y + 9$

A) $( 4 y + 3 ) ( 5 y + 3 )$
B) $( 20 y + 3 ) ( y + 3 )$
C) $( 20 y - 3 ) ( y - 3 )$
D) $( 4 y - 3 ) ( 5 y - 3 )$

Question 43

If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
$$16 x ^ { 2 } - 56 x - 32$$

A) $8 ( 2 x - 1 ) ( x + 4 )$
B) $( 16 x - 8 ) ( x + 4 )$
C) $16 x ^ { 2 } - 56 x - 32$
D) $8 ( 2 x + 1 ) ( x - 4 )$

Question 44

If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
$$- 12 x ^ { 3 } - 50 x ^ { 2 } - 50 x$$

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

Question 45

If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
$$12 x ^ { 2 } - 52 x - 40$$

A) $4 ( 3 x + 2 ) ( x - 5 )$
B) $4 ( 3 x - 2 ) ( x + 5 )$
C) $12 x ^ { 2 } - 52 x - 40$
D) $( 12 x + 8 ) ( x - 5 )$

Question 46

Factor.
$$x ^ { 5 } + 10 x ^ { 4 } + 21 x ^ { 3 }$$

A) $x ^ { 7 } \left( x ^ { 2 } + 10 x + 21 \right)$
B) $x ^ { 3 } ( x + 7 ) ( x - 3 )$
C) $x ^ { 3 } ( x - 7 ) ( x + 3 )$
D) $x ^ { 3 } ( x + 7 ) ( x + 3 )$

Question 47

If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
$$45 x ^ { 3 } - 21 x ^ { 2 } - 6 x$$

A) $x ( 3 x - 2 ) ( 15 x + 3 )$
B) $3 \left( 3 x ^ { 2 } - 2 \right) ( 5 x + 1 )$
C) $3 x ( 3 x - 2 ) ( 5 x + 1 )$
D) $x ( 9 x - 6 ) ( 5 x + 1 )$

Question 48

If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
$15 x ^ { 2 } y ^ { 2 } + 16 x y ^ { 2 } + 4 y ^ { 2 }$

A) $y ^ { 2 } ( 3 x + 2 ) ( 5 x + 2 )$
B) $y ^ { 2 } ( x + 2 ) ( 15 x + 2 )$
C) $( 5 x + 2 y ) ( 3 x + 2 y )$
D) $( 3 x + 2 y ) ( 5 x + 2 y )$

Question 49

Factor using the trial and error method
$$6 z ^ { 2 } + 5 z - 6$$

A) $( 3 z - 2 ) ( 2 z + 3 )$
B) $6 z ^ { 2 } + 5 z - 6$
C) $( 3 z + 2 ) ( 2 z - 3 )$
D) $( 6 z - 2 ) ( z + 3 )$

Question 50

Factor using the trial and error method
$$7 x ^ { 2 } + 11 x - 6$$

A) $( 7 x - 3 ) ( x + 2 )$
B) $( 7 x + 2 ) ( x - 3 )$
C) $( 7 x - 2 ) ( x + 3 )$
D) $( 7 x + 3 ) ( x - 2 )$

Question 51

Factor using the trial and error method
$$20 x ^ { 2 } + 31 x + 12$$

A) $( 4 x - 3 ) ( 5 x - 4 )$
В) $( 20 x - 3 ) ( x - 4 )$
C) $( 20 x + 3 ) ( x + 4 )$
D) $( 4 x + 3 ) ( 5 x + 4 )$

Question 52

If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
$$8 y ^ { 2 } + 36 y - 20$$

A) $( 8 y - 4 ) ( y + 5 )$
B) $4 ( 2 y + 1 ) ( y - 5 )$
C) $8 x ^ { 2 } - 36 x - 20$
D) $4 ( 2 y - 1 ) ( y + 5 )$

Question 53

Find a polynomial in factored form for the shaded region.

A)
B)
C)
D)

Question 54

Factor using the trial and error method
$$4 x ^ { 2 } - 12 x t + 9 t ^ { 2 }$$

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

Question 55

Factor using the trial and error method
$$6 z ^ { 2 } + 5 z - 6$$

A) $( 6 z + 3 ) ( z - 2 )$
B) $( 2 z + 3 ) ( 3 z - 2 )$
C) $( 2 z - 3 ) ( 3 z + 2 )$
D) $6 z ^ { 2 } + 5 z - 6$

Question 56

Factor using the trial and error method
$$10 y ^ { 2 } + 21 y + 9$$

A) $10 y ^ { 2 } + 21 y + 9$
B) $( 10 y + 3 ) ( y + 3 )$
C) $( 2 y + 3 ) ( 5 y + 3 )$
D) $( 2 y - 3 ) ( 5 y - 3 )$

Question 57

Factor using the trial and error method
$6 x ^ { 2 } - 5 x - 6$

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

Question 58

Factor using the trial and error method
$$16 x ^ { 2 } + 24 x + 9$$

A) $( 4 x - 3 ) ( 4 x - 3 )$
B) $( 16 x - 3 ) ( x - 3 )$
C) $( 16 x + 3 ) ( x + 3 )$
D) $( 4 x + 3 ) ( 4 x + 3 )$

Question 59

Factor using the trial and error method
$$16 x ^ { 2 } + 24 x + 9$$

A) $( 4 x - 3 ) ( 4 x - 3 )$
B) $( 4 x + 3 ) ( 4 x + 3 )$
C) $( 16 x + 3 ) ( x + 3 )$
D) $16 x ^ { 2 } + 24 x + 9$

Question 60

Factor using the trial and error method
$12 x ^ { 2 } - 7 x - 12$

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

Question 61

If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
$$x ^ { 2 } + 10 x y + 25 y ^ { 2 }$$

A) $( x + 5 y ) ( x - 5 y )$
B) $x ^ { 2 } + 10 x y + 25 y ^ { 2 }$
C) $( x + 5 y ) ^ { 2 }$
D) $( x - 5 y ) ^ { 2 }$

Question 62

If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
$- 50 x ^ { 3 } + 115 x ^ { 2 } - 60 x$

A) $- 5 \left( 2 x ^ { 2 } - 3 \right) ( 5 x - 4 )$
B) $x ( - 10 x + 15 ) ( 5 x - 4 )$
C) $- 5 x ( 2 x - 3 ) ( 5 x - 4 )$
D) $x ( 2 x - 3 ) ( - 25 x + 20 )$

Question 63

If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
$$s ^ { 12 } - t ^ { 16 }$$

A) $\left( s ^ { 6 } + t ^ { 8 } \right) \left( s ^ { 6 } - t ^ { 8 } \right)$
B) $\left( \mathrm { s } ^ { 10 } - \mathrm { t } ^ { 14 } \right) ^ { 2 }$
C) $\left( s ^ { 6 } - t ^ { 8 } \right) ^ { 2 }$
D) $\left( \mathrm { s } ^ { 10 } + \mathrm { t } ^ { 14 } \right) \left( \mathrm { s } ^ { 10 } - \mathrm { t } ^ { 14 } \right)$

Question 64

If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
$16 k ^ { 2 } - 121 m ^ { 2 }$

A) $( 4 \mathrm { k } + 11 \mathrm {~m} ) ^ { 2 }$
B) $( 4 k + 11 m ) ( 4 k - 11 m )$
C) $16 \mathrm { k } ^ { 2 } - 121 \mathrm {~m} ^ { 2 }$
D) $( 4 \mathrm { k } - 11 \mathrm {~m} ) ^ { 2 }$

Question 65

If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
$$49 x ^ { 2 } + 56 x y + 16 y ^ { 2 }$$

A) $( 49 x + y ) ( x + 16 y )$
B) $( 7 x - 4 y ) ^ { 2 }$
C) $( 7 x + 4 y ) ( 7 x - 4 y )$
D) $( 7 x + 4 y ) ^ { 2 }$

Question 66

If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
$$60 a ^ { 2 } + 125 a + 60$$

A) $( a + 20 ) ( 4 a + 3 )$
B) $( 3 a - 4 ) ( 4 a - 3 )$
C) $( 3 a + 4 ) ( 20 a + 15 )$
D) $( 3 a + 4 ) ( 4 a + 3 )$

Question 67

If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
$$36 x ^ { 2 } - 84 x + 49$$

A) $( 6 x - 7 ) ( 6 x + 7 )$
B) $( 36 x + 1 ) ( x + 49 )$
C) $( 6 x + 7 ) ^ { 2 }$
D) $( 6 x - 7 ) ^ { 2 }$

Question 68

If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
$$81 - w ^ { 2 }$$

A) $( 9 - w ) ^ { 2 }$
B) $( 9 + w ) ^ { 2 }$
C) $( 9 - w ) ( 9 + w )$
D) $81 - w ^ { 2 }$

Question 69

If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
$$z ^ { 2 } - 14 z + 49$$

A) $( z - 7 ) ( z + 7 )$
B) $( z - 14 ) ( z + 14 )$
C) $( z - 7 ) ^ { 2 }$
D) $( z + 7 ) ^ { 2 }$

Question 70

If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
$$a ^ { 2 } x ^ { 2 } - 1$$

A) $( a x + 1 ) ( a x - 1 )$
B) $( a x - 1 ) ^ { 2 }$
C) $( a x + 1 ) ^ { 2 }$
D) $a ^ { 2 } x ^ { 2 } - 1$

Question 71

If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
$49 - x ^ { 2 } y ^ { 2 }$

A) $( 7 + x y ) ^ { 2 }$
B) $49 - x ^ { 2 } y ^ { 2 }$
C) $( 7 - x y ) ( 7 + x y )$
D) $( 7 - x y ) ^ { 2 }$

Question 72

If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
$$49 x ^ { 2 } - 56 x y + 16 y ^ { 2 }$$

A) $( 7 x - 4 y ) ^ { 2 }$
B) $( 7 x + 4 y ) ^ { 2 }$
C) $( 49 x + 1 ) ( x + 16 )$
D) $( 7 x - 4 y ) ( 7 x + 4 y )$

Question 73

If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
$$64 x ^ { 2 } - 49$$

A) $( 8 x + 7 ) ^ { 2 }$
B) $( 8 x + 7 ) ( 8 x - 7 )$
C) $( 8 x - 7 ) ^ { 2 }$
D) $64 x ^ { 2 } - 49$

Question 74

If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
$z ^ { 2 } - 121$

A) $z ^ { 2 } - 121$
B) $( z - 11 ) ^ { 2 }$
C) $( z + 11 ) ^ { 2 }$
D) $( z + 11 ) ( z - 11 )$

Question 75

If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
$$r ^ { 2 } + 10 r + 25$$

A) $( r + 5 ) ( r - 5 )$
B) $( r - 5 ) ^ { 2 }$
C) $( \mathrm { r } + 5 ) ^ { 2 }$
D) $( r + 10 ) ( r - 10 )$

Question 76

If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
$$x ^ { 2 } - 12 x + 36$$

A) $( x - 6 ) ^ { 2 }$
B) $( x + 6 ) ^ { 2 }$
C) $( x - 12 ) ( x + 12 )$
D) $( x - 6 ) ( x + 6 )$

Question 77

If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
$$16 x ^ { 2 } - 25$$

A) $( 4 x - 5 ) ^ { 2 }$
В) $( 4 x + 5 ) ^ { 2 }$
C) $( 4 x + 5 ) ( 4 x - 5 )$
D) $16 x ^ { 2 } - 25$

Question 78

If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
$$16 - 9 x ^ { 2 }$$

A) $16 - 9 x ^ { 2 }$
В) $( 4 + 3 x ) ^ { 2 }$
D) $( 4 + 3 x ) ( 4 - 3 x )$

Question 79

If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
$$x ^ { 2 } + 8 x + 16$$

A) $x ^ { 2 } + 8 x + 16$
B) $( x + 4 ) ( x - 4 )$
C) $( x + 4 ) ^ { 2 }$
D) $( x - 4 ) ^ { 2 }$

Question 80

If possible, factor the polynomial completely. If a polynomial cannot be factored, state that it is prime.
$$12 x ^ { 2 } y ^ { 2 } + 7 x y ^ { 2 } - 12 y ^ { 2 }$$

A) $( 3 x + 4 y ) ( 4 x - 3 y )$
B) $y ^ { 2 } ( x + 4 ) ( 12 x - 3 )$
C) $y ^ { 2 } ( 3 x + 4 ) ( 4 x - 3 )$
D) $( 4 x + 4 y ) ( 3 x - 3 y )$