Deck 10: Factoring Algebraic Expressions

Question 1

Factor completely. $35 b ^ { 2 } - 13 b - 4$

A) $( 5 b - 1 ) ( 7 b - 4 )$
B) $( 35 b + 1 ) ( b - 4 )$
C) $( b + 1 ) ( 35 b - 4 )$
D) $( 5 b + 1 ) ( 7 b - 4 )$
E) $( 5 b - 1 ) ( 7 b + 4 )$

Answer 1

$( 5 b + 1 ) ( 7 b - 4 )$

Question 2

Factor completely. $6 a ^ { 2 } - 37 a - 35$

A) $( 6 a + 1 ) ( a - 35 )$
B) $( 6 a + 5 ) ( a - 7 )$
C) $( 6 a - 5 ) ( a + 7 )$
D) $( 6 a + 35 ) ( a - 1 )$
E) Not factorable

Answer 2

$( 6 a + 5 ) ( a - 7 )$

Question 3

Factor completely. $72 b x ^ { 2 } - 42 b x - 9 b$

A) $3 b ( 6 x + 1 ) ( 4 x - 3 )$
B) $b ( 6 x + 1 ) ( 4 x - 3 )$
C) $3 b ( 6 x - 1 ) ( 4 x - 6 )$
D) $3 b ( 6 x - 1 ) ( 4 x + 3 )$
E) $3 b ( 6 x - 1 ) ( 4 x - 3 )$

Answer 3

$3 b ( 6 x + 1 ) ( 4 x - 3 )$

Question 4

Factor completely. $32 m ^ { 2 } - 28 m - 9$

A) $( m + 1 ) ( 32 m - 9 )$
B) $( 4 m + 1 ) ( 8 m - 9 )$
C) $( 4 m + 1 ) ( 8 m + 9 )$
D) $( 32 m + 1 ) ( m - 9 )$
E) $( 4 m - 1 ) ( 8 m + 9 )$

Question 5

Factor completely. $5 a ^ { 2 } - 16 a - 45$

A) $( 5 a - 45 ) ( a + 1 )$
B) $( 5 a + 9 ) ( a - 5 )$
C) $( 5 a - 9 ) ( a + 5 )$
D) $( 5 a - 1 ) ( a + 45 )$
E) Not factorable

Question 6

Factor completely. $64 y ^ { 2 } - 16 y + 1$

A) $( 8 y - 1 ) ( 8 y - 1 )$
B) $( y - 1 ) ( 64 y - 1 )$
C) $( 8 y + 1 ) ( 8 y + 1 )$
D) $( 64 y - 1 ) ( y - 1 )$
E) Not factorable

Question 7

Factor completely. $18 x ^ { 2 } - 17 x + 4$

A) $( x - 1 ) ( 18 x - 4 )$
B) $( 2 x - 1 ) ( 9 x - 4 )$
C) $( 2 x - 36 ) ( 1 x - 1 )$
D) $( 18 x - 1 ) ( x - 4 )$
E) $( 2 x - 4 ) ( 9 x - 1 )$

Question 8

Factor completely. $3 a ^ { 2 } + 4 a - 15$

A) $( 3 a - 1 ) ( a + 15 )$
B) $( 3 a + 5 ) ( a - 3 )$
C) $( 3 a - 15 ) ( a + 1 )$
D) $( 3 a - 5 ) ( a + 3 )$
E) Not factorable

Question 9

Factor completely. $4 x ^ { 2 } - 4 x - 15$

A) $( 2 x + 3 ) ( 2 x - 5 )$
B) $( 4 x + 3 ) ( x - 5 )$
C) $( 2 x + 5 ) ( 2 x - 2.718282 )$
D) $( 2 x + 5 ) ( 2 x - 10 )$
E) $( 4 x + 5 ) ( 2 x - 2.718282 )$

Question 10

Factor completely. $49 x ^ { 2 } - 56 x + 16$

A) $( x + 4 ) ( 49 x + 4 )$
B) $( 7 x - 4 ) ( 7 x - 4 )$
C) $( 7 x - 16 ) ( 7 x - 4 )$
D) $( 7 x + 4 ) ( 7 x + 4 )$
E) $( 49 x - 4 ) ( x - 4 )$

Question 11

Factor completely. $320 x ^ { 3 } + 240 x ^ { 2 } + 45 x$

A) $\left( 40 x ^ { 2 } + 15 \right) ( 8 x + 3 )$
B) $5 x ( 8 x + 3 ) ( 8 x + 3 )$
C) $5 x ( 8 x - 3 ) ( 8 x - 3 )$ .
D) $\left( 40 x ^ { 2 } + 15 \right) ( 8 x + 3 )$ .
E) Not factorable

Question 12

Factor completely. $2 x ^ { 2 } + 27 x + 81$

A) $( 2 x - 9 ) ( x - 9 )$
B) $( 2 x + 81 ) ( x + 1 )$
C) $( 2 x + 9 ) ( x + 9 )$
D) $( 2 x + 1 ) ( x + 81 )$
E) Not factorable

Question 13

Factor completely. $12 x ^ { 2 } - 17 x + 6$

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

Question 14

Factor completely. $20 t ^ { 2 } + 9 t - 20$

A) $( 4 t - 5 ) ( 5 t - 4 )$
B) $( 4 t + 5 ) ( 5 t + 4 )$
C) $( 4 t + 5 ) ( 5 t - 4 )$
D) $( 4 t - 5 ) ( 5 t + 4 )$
E) $( 5 - 4 t ) ( 5 t + 4 )$

Question 15

Factor completely. $56 x ^ { 2 } - 113 x + 56$

A) $( x - 7 ) ( 56 x - 8 )$
B) $( 8 x - 7 ) ( 7 x - 8 )$
C) $( 8 x + 7 ) ( 7 x - 8 )$
D) $( 56 x - 7 ) ( x - 8 )$
E) $( 8 x + 56 ) ( 7 x - 1 )$

Question 16

Factor completely. $8 x ^ { 2 } - x - 27$

A) $( 2 x + 27 ) ( 4 x - 1 )$
B) $( 2 x + 6 ) ( 4 x - 9 )$
C) $( 2 x + 3 ) ( 4 x - 9 )$
D) $( 2 x + 1 ) ( 4 x - 27 )$
E) $( 2 x - 3 ) ( 4 x + 9 )$

Question 17

Factor completely. $8 x ^ { 2 } + 5 x - 22$

A) $( 8 x + 11 ) ( x - 1 )$
B) $( 8 x - 11 ) ( x - 2 )$
C) $( 8 x - 11 ) ( x + 2 )$
D) $( 8 x - 22 ) ( x + 1 )$
E) $( 8 x - 11 ) ( 8 x + 2 )$

Question 18

Factor completely. $- 16 x ^ { 3 } - 76 x ^ { 2 } - 18 x$

A) $- 76 x ( 4 x - 1 ) ( 2 x - 9 )$
B) $2 x ( - 4 x + 1 ) ( 2 x + 9 )$
C) $- x ( 8 x + 2 ) ( 2 x + 9 )$
D) $- 2 x ( 4 x + 1 ) ( 2 x + 9 )$
E) $- 2 x ( 4 x + 1 ) ( 4 x + 18 )$

Question 19

Factor completely. $63 y ^ { 2 } - 32 y - 63$

A) $( 63 y + 7 ) ( y - 9 )$
B) $( 9 y - 7 ) ( 7 y - 9 )$
C) $( 9 y - 7 ) ( 7 y + 9 )$
D) $( 9 y + 7 ) ( 7 y - 9 )$
E) $( y + 7 ) ( 63 y - 9 )$

Question 20

Factor completely. $2 y ^ { 4 } - 5 y ^ { 2 } - 33$

A) $\left( 2 y ^ { 2 } - 11 \right) \left( y ^ { 2 } + 3 \right)$
B) $\left( 2 y ^ { 2 } + 11 \right) \left( y ^ { 2 } - 3 \right)$
C) $( 2 y + 11 ) \left( y ^ { 2 } - 3 \right)$
D) $\left( 2 y ^ { 2 } + 1 \right) \left( y ^ { 2 } - 33 \right)$
E) $\left( 2 y ^ { 2 } + 3 \right) \left( y ^ { 2 } - 11 \right)$

Question 21

Factor completely. $28 x ^ { 2 } - 15 x + 2$

Question 22

Factor completely. $20 z ^ { 2 } + 7 z - 6$

Question 23

Factor completely. $6 a ^ { 2 } - 13 a - 44$

Question 24

Factor completely. $12 x ^ { 2 } - 17 x + 6$

Question 25

Factor completely. $4 x ^ { 2 } - 8 x - 5$

Question 26

Factor completely. Check by multiplying the factors. $p ^ { 2 } - s ^ { 2 }$

A) $( p - s ) ( p - s )$
B) $( p - s ) s$
C) $p ( p + s )$
D) $( p - s ) ( p + s )$
E) $( p + s ) s$

Question 27

Factor completely. $64 x ^ { 2 } + 48 x - 9$

Question 28

Factor completely. $63 y ^ { 2 } - 32 y - 63$

Question 29

Factor completely. $48 b x ^ { 2 } - 16 b x - 4 b$

Question 30

Factor completely. $8 m ^ { 2 } - 14 m - 9$

Question 31

Factor completely. Check by multiplying the factors. $6 c ^ { 2 } - 12 c + 6$

A) $( 6 c - 6 ) ( c - 1 )$
B) $6 ( c + 1 ) ( c + 1 )$
C) $6 ( c - 1 ) ( c + 1 )$
D) $( 6 c + 6 ) ( c + 1 )$
E) $6 ( c - 1 ) ( c - 1 )$

Question 32

Factor completely. $2 x ^ { 2 } + 27 x + 81$

Question 33

Factor completely. $3 a ^ { 2 } + 14 a - 80$

Question 34

Factor completely. Check by multiplying the factors. $b ^ { 2 } - 18 b + 81$

A) $( b - 9 ) ( b - 9 )$
B) $( b - 81 ) ( b - 1 )$
C) $( b + 9 ) ( b - 9 )$
D) $( b + 81 ) ( b + 1 )$
E) $( b + 9 ) ( b + 9 )$

Question 35

Factor completely. $20 x ^ { 2 } - 23 x + 6$

Question 36

Factor completely. $7 x ^ { 2 } + 9 x - 10$

Question 37

Factor completely. $20 x ^ { 2 } - x - 30$

Question 38

Factor completely. $121 x ^ { 2 } - 77 x + 10$

Question 39

Factor completely. $4 y ^ { 4 } - 3 y ^ { 2 } - 45$

Question 40

Factor completely. $5 a ^ { 2 } - 32 a - 21$

Question 41

Factor completely. Check by multiplying the factors. $y m ^ { 2 } - 8 y m + 16 y$

A) $y ( m - 4 y ) ( m - 4 )$
B) $y ( m - 1 ) ( m - 16 )$
C) $( y m - 4 ) ( m - 4 )$
D) $( m - 4 ) ( m - 4 )$
E) $y ( m - 4 ) ( m - 4 )$

Question 42

Factor completely. Check by multiplying the factors. $- 5 y ^ { 2 } + 40 y - 80$

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

Question 43

Factor completely. Check by multiplying the factors. $144 x ^ { 2 } - 24 x + 1$

A) $( 12 x - 1 ) ( 12 x - 1 )$
B) $( 6 x - 1 ) ( 24 x - 1 )$
C) $( 144 x - 1 ) ( x - 1 )$
D) $( 6 x + 1 ) ( 24 x + 1 )$
E) $( 12 x + 1 ) ( 12 x + 1 )$

Question 44

Factor completely. Check by multiplying the factors. $25 b ^ { 2 } - 16$

A) $( 8 b - 4 ) ( 8 b + 4 )$
B) $( 25 b - 4 ) ( b + 4 )$
C) $( 6 b - 4 ) ( 6 b + 4 )$
D) $( 5 b - 4 ) ( 5 b + 4 )$
E) $( 5 b + 4 ) ( 5 b + 4 )$

Question 45

Factor completely. Check by multiplying the factors. $m ^ { 2 } + 28 m + 196$

A) $( m + 1 ) ( m + 196 )$
B) $( m + 14 ) ( m + 14 )$
C) $( m - 1 ) ( m - 196 )$
D) $( m - 14 ) ( m + 14 )$
E) $( m - 14 ) ( m - 14 )$

Question 46

Factor completely. Check by multiplying the factors. $y ^ { 2 } - c ^ { 2 }$

Question 47

Factor completely. Check by multiplying the factors. $b ^ { 2 } - 4 b + 4$

Question 48

Factor completely. Check by multiplying the factors. $49 x ^ { 2 } - 25$

A) $( 7 x + 5 ) ( 7 x + 5 )$
B) $( 7 x - 5 ) ( 7 x + 5 )$
C) $( x - 5 ) ( 49 x + 5 )$
D) $( 7 x - 25 ) ( 7 x + 1 )$
E) $( 49 x - 5 ) ( x + 5 )$

Question 49

Factor completely. Check by multiplying the factors. $16 x ^ { 2 } - 24 x + 9$

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

Question 50

Factor completely. Check by multiplying the factors. $49 - x ^ { 2 }$

A) $( 49 + x ) ( 1 - x )$
B) $x ( 49 - x )$
C) $( 7 - x ) ( 7 + x )$
D) $( 7 - x ) ( 7 - x )$
E) $( 49 - x ) ( 1 + x )$

Question 51

Factor completely. Check by multiplying the factors. $25 - x ^ { 2 } y ^ { 2 }$

A) $( 5 - x y ) ( 5 - x y )$
B) $( 1 - x y ) ( 25 + x y )$
C) $\left( 5 - x ^ { 2 } \right) \left( 5 - y ^ { 2 } \right)$
D) $( 25 - x y ) ( 1 + x y )$
E) $( 5 + x y ) ( 5 + x y )$

Question 52

Factor completely. Check by multiplying the factors. $4 a ^ { 2 } + 40 a + 100$

A) $( 4 a - 5 ) ( a + 5 )$
B) $( 4 a - 5 ) ( 4 a + 5 )$
C) $4 ( a + 5 ) ( a + 5 )$
D) $( a + 5 ) ( a + 5 )$
E) $4 ( a - 5 ) ( a - 5 )$

Question 53

Factor completely. Check by multiplying the factors. $b ^ { 2 } - 4$

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

Question 54

Factor completely. Check by multiplying the factors. $49 x ^ { 2 } - 100 y ^ { 2 }$

A) $( 7 x - 10 y ) ( 7 x - 10 y )$
B) $( 7 x - 100 y ) ( 7 x + 1 y )$
C) $( 7 x + 10 y ) ( 7 x + 10 y )$
D) $( 49 x - 10 y ) ( 1 x + 10 y )$
E) $( 7 x - 10 y ) ( 7 x + 10 y )$

Question 55

Factor completely. Check by multiplying the factors. $- 9 x ^ { 2 } + 144 x ^ { 4 }$

A) $9 x ^ { 2 } ( 144 x - 1 ) ( x + 1 )$
B) $9 x ^ { 3 } ( 4 x - 1 ) ( 4 + 1 )$
C) $9 x ^ { 2 } ( 4 x - 1 ) ( 4 + 1 )$
D) $9 x \left( 4 x ^ { 2 } - 1 \right) ( 4 x + 1 )$
E) $9 x \left( x ^ { 2 } - 1 \right) ( 16 x + 1 )$

Question 56

Factor completely. Check by multiplying the factors. $y ^ { 2 } - 49$

A) $( y - 49 ) ( y + 1 )$
B) $( y - 7 ) ( y - 7 )$
C) $( y - 7 ) ( y + 7 )$
D) $( y - 1 ) ( y + 49 )$
E) $( y + 7 ) ( y + 7 )$

Question 57

Factor completely. Check by multiplying the factors. $16 x ^ { 2 } + 24 x + 9$

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

Question 58

Factor completely. Check by multiplying the factors. $16 x ^ { 2 } - 289$

A) $( 4 x + 17 ) ( 4 x + 17 )$
B) $( 4 x - 17 ) ( 4 x + 17 )$
C) $( x - 17 ) ( 4 x + 17 )$
D) $( 4 x - 17 ) ( 4 x + 4 )$
E) $( 17 x - 17 ) ( 4 x + 17 )$

Question 59

Factor completely. Check by multiplying the factors. $4 x ^ { 2 } - 81$

Question 60

Factor completely. Check by multiplying the factors. $y ^ { 2 } - 12 y + 36$

A) $( y + 6 ) ( y - 6 )$
B) $( y - 6 ) ( y - 6 )$
C) $( y + 5 ) ( y + 7 )$
D) $( y + 6 ) ( y + 6 )$
E) $( y - 1 ) ( y - 36 )$

Question 61

Factor completely. Check by multiplying the factors. $2 c ^ { 2 } - 8 c + 8$

Question 62

Factor completely. Check by multiplying the factors. $- 3 y ^ { 2 } + 18 y - 27$

Question 63

Factor. $2 x y - 8 y$

A) $2 y ( x - 4 )$
B) $2 x ( x - 4 )$
C) $y ( 2 x - 8 )$
D) $2 y ( y - 4 )$
E) $2 y ( x y - 4 )$

Question 64

Factor. $17 x ^ { 2 } - 17 x$

A) $17 \left( x ^ { 2 } - 13 \right)$
B) $17 \left( x ^ { 2 } - x \right)$
C) $17 x ( 17 x - 1 )$
D) $17 x ( x - 17 )$
E) $17 x ( x - 1 )$

Question 65

Factor completely. Check by multiplying the factors. $81 x ^ { 2 } - 25$

Question 66

Factor completely. Check by multiplying the factors. $25 b ^ { 2 } - 4$

Question 67

Factor. $\mathrm { wx } + \mathrm { wy }$

A) $\mathrm { w } ( \mathrm { w } x + y )$
B) $\mathrm { w } ( \mathrm { w } x + y )$ .
C) $( x + y )$
D) $\mathrm { w } ( x + y )$
E) $\mathrm { w } ( \mathrm { w } x + \mathrm { w } y )$

Question 68

Factor completely. Check by multiplying the factors. $y ^ { 2 } - 14 y + 49$

Question 69

Factor. $a - 2 a ^ { 9 }$

A) $a \left( 1 - 2 a ^ { 8 } \right)$
B) $2 a \left( 1 - a ^ { 7 } \right)$
C) $a ( 1 - 2 a )$
D) $a \left( 1 - 2 a ^ { 9 } \right)$
E) $a \left( 1 - 2 a ^ { 12 } \right)$

Question 70

Factor completely. Check by multiplying the factors. $16 - x ^ { 2 } y ^ { 2 }$

Question 71

Factor. $8 a + 8$

A) $8 ( a + 1 )$
B) $8 ( a + 8 )$
C) $( a + 8 )$
D) $8 ( 8 a + 1 )$
E) $( a + 1 )$

Question 72

Factor. $24 a ^ { 2 } - 24 b ^ { 2 }$

A) $24 \left( a ^ { 2 } - b ^ { 2 } \right)$
B) $24 a b ( a - b )$
C) $24 a \left( a - b ^ { 2 } \right)$
D) $24 b \left( a ^ { 2 } - b \right)$
E) $24 a b \left( a ^ { 2 } - b \right)$

Question 73

Factor completely. Check by multiplying the factors. $b ^ { 2 } - 4$

Question 74

Factor completely. Check by multiplying the factors. $y ^ { 2 } - 64$

Question 75

Factor. $s ^ { 3 } + 7 s ^ { 2 } + 29 s$

A) $s \left( s ^ { 2 } + 7 s + 29 s \right)$
B) $s ^ { 2 } \left( s ^ { 2 } + 7 s + 29 \right)$
C) $s ^ { 3 } ( 1 + 7 s + 29 )$
D) $s \left( s ^ { 2 } + 7 s + 29 \right)$
E) $s \left( s ^ { 3 } + 7 s ^ { 2 } + 29 \right)$

Question 76

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

A) $4 x \left( x ^ { 2 } - 3 \right)$
B) $x ( 4 x - 4 )$
C) $4 x ( 4 x - 16 )$
D) $4 x ( x - 3 )$
E) $9 x ( x - 4 )$

Question 77

Factor. $7 y - 35$

A) $7 y ( y - 5 )$
B) $7 ( y - 5 )$
C) $7 y ( 7 y - 5 )$
D) $7 ( y - 35 )$
E) $5 ( y - 7 )$

Question 78

Factor. $4 x ^ { 4 } + 20 x ^ { 3 } + 24 x ^ { 2 }$

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

Question 79

Factor completely. Check by multiplying the factors. $36 - x ^ { 2 }$

Question 80

Factor. $10 x y - 2 x ^ { 2 } y ^ { 2 }$

A) $2 y ( 5 - x )$
B) $2 x ^ { 2 } ( 5 - x y )$
C) $2 x ( 5 - x y )$
D) $2 x y ( 5 - x y )$
E) $2 y ( 5 - x y )$