Deck 5: Polynomials: an Introduction to Algebra

Question 1

Divide. $\frac { a ^ { 10 } - a ^ { 9 } - a ^ { 8 } } { a ^ { 4 } }$

A) $a ^ { 6 } - a ^ { 3 } + a ^ { 4 }$
B) $a ^ { 6 } - a ^ { 5 } - a ^ { 4 }$
C) $a ^ { 14 } - a ^ { 13 } - a ^ { 12 }$
D) $a ^ { 5 } + a ^ { 3 } - a ^ { 4 }$
E) $a ^ { 5 } - a ^ { 5 } - a ^ { 7 }$

Answer 1

$a ^ { 6 } - a ^ { 5 } - a ^ { 4 }$

Question 2

Divide. $\left( 69 x ^ { 4 } y ^ { 4 } \right) \div \left( - 23 x ^ { 4 } y ^ { 5 } \right)$

A) $- \frac { 3 } { y }$
B) $- 3 y$
C) $- \frac { 8 } { y ^ { 2 } }$
D) $- 3 x ^ { 8 } y ^ { 9 }$
E) $- \frac { 3 x ^ { 4 } } { y }$

Answer 2

$- \frac { 3 } { y }$

Question 3

Divide the monomials. $\frac { 35 z ^ { 7 } } { 7 z ^ { 2 } }$

A) $5 z ^ { 5 }$
B) $5 z ^ { 9 }$
C) $7 z ^ { 9 }$
D) $49 z ^ { 5 }$
E) $28 z ^ { 5 }$

Answer 3

$5 z ^ { 5 }$

Question 4

Divide. $\frac { - 14 a ^ { 8 } b ^ { 3 } } { - 12 a ^ { 4 } b ^ { 8 } }$

A) $\frac { 7 a ^ { 12 } } { 6 b ^ { 11 } }$
B) $\frac { 7 a ^ { 4 } } { 6 b ^ { 5 } }$
C) $\frac { 6 a ^ { 4 } } { 7 b ^ { 5 } }$
D) $\frac { 7 b ^ { 5 } } { 6 a ^ { 4 } }$
E) $\frac { 6 b ^ { 5 } } { 7 a ^ { 4 } }$

Question 5

Divide. $\left( z ^ { 7 } + z ^ { 6 } + z ^ { 5 } \right) \div z ^ { 5 }$

A) $z ^ { 2 } + z + 1$
B) $z ^ { 2 }$
C) $z ^ { 2 } + z$
D) $z + 1$
E) $z ^ { 14 } + z ^ { 13 } + z ^ { 12 }$

Question 6

Divide. $\frac { 32 x ^ { 19 } } { 24 x ^ { 3 } }$

A) $\frac { 4 } { 3 x ^ { 16 } }$
B) $\frac { 3 x ^ { 22 } } { 4 }$
C) $\frac { 4 x ^ { 16 } } { 3 }$
D) $\frac { 3 x ^ { 16 } } { 4 }$
E) $\frac { 4 x ^ { 22 } } { 3 }$

Question 7

Divide. $\frac { 1 - 10 z ^ { 2 } - 8 z ^ { 4 } } { 2 z ^ { 2 } }$

A) $\frac { 1 } { 2 z ^ { 2 } } - 4 z ^ { 2 }$
B) $\frac { 1 } { 2 z ^ { 2 } } - 5 z ^ { 4 } - 4 z ^ { 2 }$
C) $\frac { 1 } { 2 z ^ { 2 } } - 4$
D) $\frac { 1 } { 2 z ^ { 2 } } - 5 - 4 z ^ { 2 }$
E) $\frac { 1 } { 2 z } - 5 - 4 z ^ { 2 }$

Question 8

Divide. $\frac { b z ^ { 4 } - b z ^ { 3 } + b z ^ { 2 } - 7 b z } { - b z }$

A) $- z ^ { 3 } + z ^ { 2 } - z + 7$
B) $- b z ^ { 3 } + b z ^ { 2 } + b z + b + 7$
C) $- z ^ { 3 } + z ^ { 2 } + z + 7$
D) $- z ^ { 3 } + z ^ { 2 } - z + 7$ .
E) $- b z ^ { 3 } + b z ^ { 2 } - b z + 7$

Question 9

Divide. $\left( - 272 x ^ { 2 } z ^ { 3 } \right) \div \left( 340 x ^ { 5 } y ^ { 2 } z \right)$

A) $\frac { 4 z } { 5 x ^ { 3 } y ^ { 2 } }$
B) $\frac { - 4 z ^ { 3 } } { 5 x ^ { 2 } y ^ { 2 } }$
C) $\frac { - 4 z ^ { 2 } } { 5 x ^ { 3 } y ^ { 2 } }$
D) $- 4 z ^ { 2 } x ^ { 3 }$
E) $\frac { - 4 x ^ { 3 } } { 5 z ^ { 2 } y ^ { 2 } }$

Question 10

Divide. $\frac { 25 x ^ { 8 } } { - 40 x ^ { 3 } y ^ { 2 } }$

A) $- \frac { 5 x ^ { 5 } y } { 8 }$
B) $- \frac { 3 x ^ { 2 } } { 2 }$
C) $- x ^ { 5 } y ^ { 2 }$
D) $- \frac { 5 x ^ { 5 } } { 8 y ^ { 2 } }$
E) $- \frac { 2 x ^ { 3 } } { 3 y ^ { 2 } }$

Question 11

Divide. $\left( 12 b ^ { 3 } - 36 b ^ { 2 } - 3 b \right) \div ( - 3 b )$

A) $4 b ^ { 2 } - 12 b + 1$
B) $- 4 b ^ { 2 } + 12 b + 1$
C) $b ^ { 2 }$
D) $b + 1$
E) $b ^ { 14 } + b ^ { 13 } + b ^ { 12 }$

Question 12

Divide. $\frac { 14 y ^ { 5 } - 12 y ^ { 3 } - 10 y } { 2 y ^ { 2 } }$

A) $7 y ^ { 2 } - 6 y - \frac { 6 } { y }$
B) $7 y ^ { 3 } - 6 y ^ { 2 } - 5 y$
C) $7 y ^ { 3 } - \frac { 6 } { y } - 5 y$
D) $7 y ^ { 2 } - 6 y - 5$
E) $7 y ^ { 3 } - 6 y - \frac { 5 } { y }$

Question 13

Divide. $\frac { b ^ { 2 } c } { b c ^ { 2 } }$

A) $\frac { c } { b }$
B) $\frac { b } { c }$
C) $C$
D) $b$
E) $b c$

Question 14

Reduce the rational expression to lowest terms. $\frac { - 7 w ^ { 7 } } { 2 w ^ { 5 } }$

A) $\frac { 7 w ^ { 2 } } { 2 }$
B) $- \frac { 7 w ^ { 12 } } { 2 }$
C) $- \frac { 7 w ^ { 3 } } { 2 }$
D) $- \frac { 7 w ^ { 2 } } { 2 }$
E) $\frac { 7 w ^ { 3 } } { 2 }$

Question 15

Divide. $\frac { - 155 r s ^ { 9 } } { - 31 r ^ { 2 } s ^ { 8 } }$

A) $\text { 5rs }$
B) $\frac { 55 } { r }$
C) $- \frac { r } { 5 s }$
D) $\frac { 5 r } { s }$
E) $\frac { 5 s ^ { 2 } } { r }$

Question 16

Divide. $\frac { 224 x ^ { 4 } y ^ { 2 } z ^ { 3 } - 168 x ^ { 3 } y ^ { 3 } z ^ { 4 } - 112 x y ^ { 4 } z ^ { 2 } } { 28 x y ^ { 2 } z ^ { 2 } }$

A) $8 x ^ { 3 } z - 6 x y ^ { 2 } z ^ { 2 } - 4 y ^ { 4 }$
B) $8 x ^ { 3 } z - 6 x y ^ { 2 } z ^ { 2 } + 4 y ^ { 4 }$
C) $8 x ^ { 3 } z ^ { 3 } - 6 x ^ { 2 } y z ^ { 2 } - 4 y$
D) $8 x ^ { 3 } z - 6 x ^ { 2 } y z ^ { 2 } - 4 y ^ { 2 }$
E) $8 x ^ { 2 } z - 6 x ^ { 3 } y z ^ { 2 } + 4 y ^ { 2 }$

Question 17

Divide. $\frac { 24 w ^ { 4 } r ^ { 4 } + 32 w ^ { 3 } r ^ { 3 } - 40 w ^ { 2 } r ^ { 2 } } { 8 w ^ { 3 } r ^ { 3 } }$

A) $3 w r + 5 - \frac { 4 } { w r }$
B) $3 w r + 4 w - \frac { 5 } { w r ^ { 3 } }$
C) $3 w r ^ { 2 } + 4 - \frac { 5 } { w r }$
D) $3 w r + 5 + \frac { 4 } { w r }$
E) $3 w r + 4 - \frac { 5 } { w r }$

Question 18

Divide. $\left( 4 a ^ { 3 } b \right) \div \left( 2 a b ^ { 2 } \right)$

A) $\frac { 2 a ^ { 2 } } { b }$
B) $\frac { 2 b } { a ^ { 2 } }$
C) $\frac { 2 a } { b }$
D) $2 a ^ { 4 } b ^ { 3 }$
E) $\frac { a } { 2 b }$

Question 19

Divide. $\frac { 108 x ^ { 2 } y ^ { 3 } + 36 x ^ { 3 } y ^ { 4 } - 12 x y ^ { 3 } } { 3 x y ^ { 3 } }$

A) $36 x ^ { 2 } + 108 x y - 1$
B) $4 x + 12 x ^ { 2 } y - 36$
C) $36 x - 12 x y ^ { 2 } - 4$
D) $36 x - 12 x ^ { 2 } y - 4$
E) $36 x + 12 x ^ { 2 } y - 4$

Question 20

Divide. $\left( - 130 m ^ { 3 } n \right) \div \left( 26 m ^ { 2 } n \right)$

A) $- 5 m n$
B) $5 m ^ { 2 }$
C) $6 m n ^ { 2 }$
D) $- 6 m ^ { 2 }$
E) $- 5 m$

Question 21

Reduce the rational expression to lowest terms. $\frac { - 7 w ^ { 6 } } { 4 w ^ { 4 } }$

Question 22

Remove the parentheses from the expression. $a + ( - b + c )$

A) -a + b - c
B) a - b + c
C) a - b - c
D) a + b - c
E) a + b + c

Question 23

Remove the parentheses from the expression. $a - ( - b + c )$

A) a - b + c
B) a + b - c
C) a - b - c
D) -a - b + c
E) a + b + c

Question 24

Divide. $\frac { b z ^ { 4 } - b z ^ { 3 } + b z ^ { 2 } - 4 b z } { - b z }$

Question 25

Divide. $\left( - 296 x ^ { 2 } z ^ { 3 } \right) \div \left( 370 x ^ { 5 } y ^ { 2 } z \right)$

Question 26

Remove the parentheses from the expression. $( 2 x + 4 ) + ( 3 y + 4 r )$

A) 2x + 4 - 3y - 4r
B) 2x + 4 + 4y + 4r
C) 2x + 4 - 4y + 4r
D) 2x + 4 + 3y + 4r
E) 2x + 4 + 3y - 4r

Question 27

Divide. $\frac { - 18 a ^ { 6 } b ^ { 4 } } { - 16 a ^ { 2 } b ^ { 9 } }$

Question 28

Divide. $\frac { - 165 r s ^ { 7 } } { - 33 r ^ { 2 } s ^ { 6 } }$

Question 29

Remove the parentheses from the expression. $x - ( y - z + 3 )$

A) 3x - y - z - 3
B) x - y + z - 3
C) x + y + z - 3
D) x - y - z - 3
E) 3x + y - z - 3

Question 30

Divide. $\frac { 20 x ^ { 4 } } { - 32 x ^ { 2 } y ^ { 2 } }$

Question 31

Divide. $\left( 6 z ^ { 3 } - 18 z ^ { 2 } - 3 z \right) \div ( - 3 z )$

Question 32

Divide. $\left( 4 a ^ { 3 } b \right) \div \left( 2 a b ^ { 2 } \right)$

Question 33

Divide. $\frac { 45 w ^ { 4 } r ^ { 4 } + 54 w ^ { 3 } r ^ { 3 } - 63 w ^ { 2 } r ^ { 2 } } { 9 w ^ { 3 } r ^ { 3 } }$

Question 34

Divide. $\frac { b ^ { 8 } - b ^ { 7 } - b ^ { 6 } } { b ^ { 4 } }$

Question 35

Divide. $\frac { c ^ { 2 } d } { c d ^ { 2 } }$

Question 36

Divide. $\frac { 54 x ^ { 2 } y ^ { 3 } + 18 x ^ { 3 } y ^ { 4 } - 6 x y ^ { 3 } } { 3 x y ^ { 3 } }$

Question 37

Divide the monomials. $\frac { 24 x ^ { 5 } } { 6 x ^ { 3 } }$

Question 38

Divide. $\left( - 58 m ^ { 5 } n \right) \div \left( 29 m ^ { 4 } n \right)$

Question 39

Divide. $\frac { 1 - 16 x ^ { 2 } - 12 x ^ { 4 } } { 4 x ^ { 2 } }$

Question 40

Divide. $\frac { 16 x ^ { 14 } } { 12 x ^ { 2 } }$

Question 41

Simplify by first removing the parentheses and then combining the like terms. $6 x - 7 ( 4 - x )$

A) 5x - 7
B) 5x + 28
C) 13x - 7
D) 13x - 28
E) 5x - 28

Question 42

Simplify by first removing the parentheses and then combining the like terms. $0.85 ( x + 3 ) - 0.25 ( 2 x + 27 )$

A) 0.35x - 4.2
B) 9.45x - 4.2
C) 0.35x - 9.3
D) 0.35x + 9.3
E) 4.2x - 0.35

Question 43

Combine the like terms. $7 x + 4.9 x - 17.8 x + 6.6 x$

A) 36.3x
B) 5.6x
C) 29.7x
D) 26.5x
E) 0.7x

Question 44

Remove the parentheses from the expression. $( 3 x + y ) - ( 2 z + 7 ) - ( 3 r - 5 s + 2 )$

A) 3x + y - 2z - 9 - 3r + 5s
B) -3x - y - 2z - 9 - 3r + 5s
C) 3x + y + 2z + 5 - 3r + 5s
D) 3x + y - 2z - 5- 3r + 5s
E) -3x - y + 2z + 5 - 3r + 5s

Question 45

Combine the like terms. $8 x ^ { 2 } y - 6 x y - y ^ { 2 } - 2 x ^ { 2 } - 6 x ^ { 2 } y + 6 y ^ { 2 }$

A) 8x ² y - 6xy + 2y - 2x ²
B) -2x ² y - 6xy + 5y ² - 2x ²
C) 2x ² y - 6xy + 5y ² - 2x ²
D) 8x ² y - 6xy + 6y ² - 2x ²
E) 2x ² y - 6xy + 3y ² - 2x ²

Question 46

Remove the parentheses from the expression. $a - ( b - c )$

Question 47

Simplify by first removing the parentheses and then combining the like terms. $7 x - ( 3 - 5 x )$

A) 2x - 3
B) 12x - 3
C) 15x
D) 12x - 8
E) 3x - 12

Question 48

Simplify by first removing the parentheses and then combining the like terms. x = __________

Question 49

Simplify by first removing the parentheses and then combining the like terms. $( 5 - 4 x ) + ( 4 x + 9 )$

A) 4x + 5
B) 8
C) 8x + 14
D) 14x
E) 14

Question 50

Simplify by first removing the parentheses and then combining the like terms. $- 14 \left( 8 x ^ { 2 } - 2 y ^ { 2 } \right)$

A) 112x ² + 28y ²
B) -112x ² + 28y ²
C) 28x ² - 112y ²
D) -28x ² + 112y ²
E) -112x + 28y

Question 51

Simplify by first removing the parentheses and then combining the like terms. $- ( x - 9 ) - 9 ( 9 + x )$

A) -72x - 10
B) -8x + 72
C) -10x - 72
D) -8x - 72
E) 10x - 72

Question 52

Simplify by first removing the parentheses and then combining the like terms. $( 4.1 x - 5.7 ) - ( - 0.9 x + 7.1 )$

A) 5x + 12.8
B) 3.2x - 12.8
C) 5x - 12.8
D) 3.2x - 5
E) 3.2x - 1.4

Question 53

Combine the like terms. $2 x ^ { 2 } + 12 x + 6 x ^ { 2 } - 10 x$

A) 8x ² + 22x
B) 8x+2
C) 8x ² +2x
D) 8x ² + 4x
E) 8x ² + 8x

Question 54

Simplify by first removing the parentheses and then combining the like terms. $( x + 8 ) - 4 ( 2 x - 7 )$

A) -29x + 20
B) 7x - 20
C) -7x + 20
D) -9x + 36
E) -7x + 36

Question 55

Simplify by first removing the parentheses and then combining the like terms.   $6 - ( y + 9 ) + ( 5 y - 6 )$

A) $9 y - 4$
B) $- 9 y - 9$
C) $- y - 21$
D) $4 y - 9$
E) $4 y + 3$

Question 56

Remove the parentheses from the expression. $a + ( b - c )$

Question 57

Simplify by first removing the parentheses and then combining the like terms. $\left( \frac { 9 } { 16 } x - 1 \right) + \left( - \frac { 1 } { 2 } x - \frac { 2 } { 5 } \right)$

A) $- \frac { 1 } { 16 } x - 1 \frac { 1 } { 5 }$
B) $\frac { 1 } { 16 } x - \frac { 4 } { 5 }$
C) $\frac { 1 } { 16 } x - 1 \frac { 2 } { 5 }$
D) $\frac { 1 } { 16 } x + 1 \frac { 1 } { 5 }$
E) $- \frac { 1 } { 16 } x - 1 \frac { 4 } { 5 }$

Question 58

Remove the parentheses from the expression. $( 4 x + 6 y - 9 ) + ( - 2 z + 5 w + 3 )$

A) 4x + 6y - 2z - 5w - 12
B) 4x + 6y + 2z + 5w - 6
C) 4x + 6y - 2z + 5w - 6
D) 4x + 6y + 2z - 5w - 12
E) 4x - 6y - 2z - 5w - 6

Question 59

Remove the parentheses from the expression. $x - ( - y + z + 3 )$

Question 60

Remove the parentheses from the expression and simplify. $( - 5 x - 3 y - 2 ) - ( 6 z - 3 w - 5 )$

A) -5x - 3y - 6z - 3w + 3
B) -5x - 3y - 6z + 3w + 7
C) -5x - 3y - 6z + 3w - 7
D) -5x - 3y - 6z + 3w + 3
E) -5x - 3y - 6z - 3w - 7

Question 61

Simplify by first removing the parentheses and then combining the like terms. $- 13 \left( 3 x ^ { 2 } - 5 y ^ { 2 } \right)$

Question 62

Simplify by first removing the parentheses and then combining the like terms. $- ( x - 9 ) - 6 ( 6 + x )$

Question 63

Remove the parentheses from the expression. $( 2 x + 4 ) + ( 3 y - 4 r )$

Question 64

Simplify by first removing the parentheses and then combining the like terms. $( 0.8 x - 2.5 ) - ( - 4.1 x + 3.9 )$

Question 65

Remove the parentheses from the expression and simplify. $( 4 x + 6 y - 9 ) - ( - 2 z + 5 w + 3 )$

Question 66

Simplify by first removing the parentheses and then combining the like terms. $2 x - 7 ( 3 - x )$

Question 67

Combine the like terms. $2.7 x + 6.4 x - 19.1 x + 7.4 x$

Question 68

Simplify by first removing the parentheses and then combining the like terms. $8 x - ( 7 - 5 x )$

Question 69

Simplify by first removing the parentheses and then combining the like terms. $7 - ( y + 9 ) + ( 6 y - 5 )$

Question 70

Simplify by first removing the parentheses and then combining the like terms. $\left( \frac { 9 } { 16 } x - 1 \right) + \left( - \frac { 1 } { 2 } x - \frac { 1 } { 3 } \right)$

Question 71

Evaluate the expression. $[ ( - 3 ) ( 2 ) + 3 ( - 3 ) ] [ 6 ( - 5 ) - 7 ( - 3 ) ] ^ { 2 }$

A) 387
B) -735
C) 18,225
D) -39,015
E) -1,215

Question 72

Evaluate the expression. ( $- 8$ ) $( - 2 ) ^ { 3 }$ + $7$ ( $- 2$ ) $\div 14$

A) 4,095
B) -65
C) 3.6
D) 63
E) 65

Question 73

Remove the parentheses from the expression and simplify. $( - 5 x - 3 y - 2 ) - ( 6 z + 3 w - 5 )$

Question 74

Simplify by first removing the parentheses and then combining the like terms. $( x + 5 ) - 10 ( 7 x - 2 )$

Question 75

Remove the parentheses from the expression and simplify. $( 3 x + y ) - ( 2 z + 7 ) - ( 3 r - 5 s + 2 )$

Question 76

Evaluate the expression. $36 \div ( - 9 ) ( 4 ) ^ { 2 } + 5 ( - 4 - 2 ) ^ { 2 } - ( - 4 ) ^ { 3 }$

A) -30
B) -52
C) 180
D) 52
E) 34

Question 77

Combine the like terms. $5 x ^ { 2 } y - 3 x y - y ^ { 2 } - 6 x ^ { 2 } - 3 x ^ { 2 } y + 3 y ^ { 2 }$

Question 78

Evaluate the expression. $( - 378 ) \div ( - 3 ) \div ( - 7 ) \div ( - 6 ) - ( - 6 ) ( - 8 ) ( - 3 )$

A) -141
B) 36.0
C) 147
D) -2
E) 141

Question 79

Combine the like terms. $5 x ^ { 2 } + 16 x + 7 x ^ { 2 } - 4 x$

Question 80

Evaluate the expression. $4 ( - 7 ) \div ( - 28 ) - ( - 81 ) \div 9$

A) 8
B) 9.1
C) -8
D) 0.8
E) 10