Deck 6: Exponents and Polynomials

Question 1

Subtract the polynomials using a horizontal format. $10 z ^ { 5 } - 6 z + 5 \text { from } 5 z ^ { 5 } + 3 z + 8$

A) $5 z ^ { 5 } - 9 z - 3$
B) $- 5 z ^ { 5 } - 9 z + 3$
C) $5 z ^ { 5 } + 9 z - 3$
D) $- 5 z ^ { 5 } + 9 z + 3$

Answer 1

$- 5 z ^ { 5 } + 9 z + 3$

Question 2

Add the polynomials. $5 z ^ { 3 } + 9 z + 10 \text { and } - 5 z ^ { 3 } - 7 z + 11$

A) $10 z ^ { 3 } + 2 z + 21$
B) $2 z + 21$
C) $2 z - 21$
D) $14 z + 21$
E) $z ^ { 3 } + 2 z + 21$

Answer 2

$2 z + 21$

Question 3

Add the polynomials. $7 x + 12,9 x ^ { 4 } + 4 x + 12 \text { and } 10 x ^ { 4 } - 6 x + 15$

A) $21 x ^ { 4 } + 5 x + 44$
B) $19 x ^ { 4 } + 8 x + 44$
C) $19 x ^ { 4 } + 5 x + 39$

Answer 3

$19 x ^ { 4 } + 5 x + 39$

Question 4

A trinomial has three terms, a binomial has two terms, and a monomial has one term.

Question 5

Add the polynomials. $5 p ^ { 5 } + 3 p + 10 \text { and } - 9 p ^ { 5 } - 10 p + 15$

A) $14 p ^ { 5 } - 7 p + 25$
B) $- 4 p ^ { 5 } - 7 p + 25$
C) $- 4 p ^ { 5 } + 7 p - 25$
D) $- 4 p ^ { 10 } - 7 p ^ { 2 } - 25$
E) $14 p ^ { 5 } + 7 p + 25$

Question 6

The degree of a monomial is the sum of the exponents of the literal factors.

Question 7

Determine the degree of the polynomial. $3 p ^ { 5 } + 10 p ^ { 4 } + 13 p$

A) 20
B) 21
C) 5
D) 10
E) 4

Question 8

The degree of the polynomial is the sum of all the exponents.

Question 9

Subtract the polynomials using a horizontal format. $9 z + 13 \text { from } 6 z + 3$

A) $3 z - 10$
B) $- 3 z + 10$
C) $- 3 z - 10$
D) $3 z + 10$

Question 10

Add the polynomials. $5 p ^ { 5 } + 3 p + 10 \text { and } - 9 p ^ { 5 } - 10 p + 15$

A) $14 p ^ { 5 } + 7 p + 25$
B) $- 4 p ^ { 5 } + 7 p - 25$
C) $- 4 p ^ { 5 } - 7 p + 25$
D) $14 p ^ { 5 } - 7 p + 25$
E) $- 4 p ^ { 10 } - 7 p ^ { 2 } - 25$

Question 11

Determine the degree of the polynomial. $3 y ^ { 5 } + 8 y ^ { 3 } + 11 y$

A) 9
B) 3
C) 5
D) 15

Question 12

Add the polynomials. $3 y + 9 \text { and } 12 y + 3$

A) 12 y + 15
B) 15 y + 12
C) 27 y + 12

Question 13

Add the polynomials. $6 z ^ { 4 } + 9 z + 10 \text { and } - 6 z ^ { 4 } - 7 z + 10$

A) $2 z - 20$
B) $2 z + 20$
C) $12 z ^ { 4 } + 2 z + 20$

Question 14

Determine the degree of the polynomial. $2 y ^ { 5 } n ^ { 4 } + 7 y ^ { 5 } n$

A) 4
B) 21
C) 5
D) 9
E) 20

Question 15

Add the polynomials. $7 x + 8 \text { and } 15 x + 2$

A) 10 x + 22
B) 22 x + 32
C) 32 x + 22
D) 22 x + 10
E) 32 x + 10

Question 16

Subtract the polynomials using a horizontal format. $3 p ^ { 3 } - 10 p ^ { 2 } + 4 \text { from } 10 p ^ { 3 } + 5 p ^ { 2 } + 6$

A) $7 p ^ { 3 } + 15 p ^ { 2 } - 2$
B) $- 7 p ^ { 3 } + 15 p ^ { 2 } + 2$
C) $- 7 p ^ { 3 } - 15 p ^ { 2 } - 2$
D) $7 p ^ { 3 } + 15 p ^ { 2 } + 2$

Question 17

The sum of a monomial and a binomial is always a trinomial.

Question 18

Determine the degree of the polynomial. $10 z ^ { 3 } l ^ { 5 } + 5 z ^ { 3 } l$

A) 15
B) 8
C) 5
D) 3

Question 19

Add the polynomials. $5 z ^ { 2 } + 4 z + 10 \text { and } - 10 z ^ { 2 } - 8 z + 13$

A) $- 5 z ^ { 4 } - 4 z ^ { 2 } - 23$
B) $- 5 z ^ { 2 } + 4 z - 23$
C) $- 5 z ^ { 2 } - 4 z + 23$

Question 20

Subtract the polynomials using a horizontal format. $- 11 p ^ { 4 } - 9 p ^ { 3 } + 2 \text { from } 3 p ^ { 4 } + 4 p ^ { 3 } + 6$

A) $- 14 p ^ { 4 } - 13 p ^ { 3 } - 4$
B) $14 p ^ { 4 } - 13 p ^ { 3 } + 4$
C) $- 14 p ^ { 4 } + 13 p ^ { 3 } - 4$
D) $14 p ^ { 4 } + 13 p ^ { 3 } + 4$

Question 21

Subtract the polynomials using a vertical format. $- 2 z - 7 \text { from } 9 z + 1$

A) $7 z + 8$
B) $7 z - 8$
C) $- 11 z + 8$
D) $11 z + 8$
E) $11 z - 8$

Question 22

Perform the indicated operations. $8 p - \{ 7 p - [ 2 p - ( 9 p - 16 ) ] \}$

A) $6 p + 16$
B) $- 6 p - 16$
C) $- 6 p + 1$
D) $6 p - 16$
E) $- 6 p + 16$

Question 23

Subtract the polynomials using a horizontal format. $8 x + 17 \text { from } 4 x + 5$

A) $- 4 x + 12$
B) $- 4 x - 12$
C) $12 x + 22$
D) $4 x + 12$
E) $4 x - 12$

Question 24

Perform the indicated operations. $( 3 z + 3 ) - ( 8 z - 11 ) + ( 9 z + 3 )$

A) $4 z + 17$
B) $4 z - 17$
C) $- 4 z - 17$
D) $- 4 z + 17$

Question 25

Subtract the polynomials using a vertical format. $- 4 z ^ { 4 } - 9 \text { from } - 9 z ^ { 4 } + 3$

A) $- 5 z ^ { 4 } - 12$
B) $5 z ^ { 4 } - 12$
C) $- 5 z ^ { 4 } + 12$
D) $5 z ^ { 4 } + 12$

Question 26

Perform the indicated operations. $12 x - [ 6 x - ( 7 x - 4 ) ]$

A) $- 13 x - 4$
B) $13 x - 4$
C) $13 x + 4$

Question 27

Perform the indicated operations. $4 z - \{ 9 z - [ 2 z - ( 8 z - 16 ) ] \}$

A) $- 11 z + 16$
B) $- 11 z - 16$
C) $11 z - 16$
D) $11 z + 16$

Question 28

Perform the indicated operations. $( n - 3 ) - \left( 7 n ^ { 2 } - n + 7 \right) + \left( n ^ { 2 } - 2 \right)$

A) $- 6 n ^ { 2 } + 12$
B) $- 6 n ^ { 2 } - 12$
C) $6 n ^ { 2 } + 2 n - 12$
D) $- 6 n ^ { 2 } + 2 n + 12$
E) $- 6 n ^ { 2 } + 2 n - 12$

Question 29

Perform the indicated operations. $\left( x ^ { 2 } - 8 x - 4 \right) + \left( 8 x ^ { 2 } - 2 x - 4 \right) - \left( 3 x ^ { 2 } - 8 x - 3 \right)$

A) $6 x ^ { 2 } - 2 x - 11$
B) $6 x ^ { 2 } + 2 x - 5$
C) $6 x ^ { 2 } - 2 x - 5$
D) $- 6 x ^ { 2 } - 2 x + 11$
E) $6 x ^ { 2 } - 2 x + 5$

Question 30

Perform the indicated operations. $( 10 x + 6 ) - ( 5 x - 2 ) + ( 4 x + 4 )$

A) $9 x + 8$
B) $- 9 x - 8$
C) $- 9 x + 12$
D) $9 x + 12$
E) $9 x - 12$

Question 31

Perform the indicated operations. $( n - 5 ) - \left( 8 n ^ { 2 } - n + 1 \right) + \left( n ^ { 2 } - 9 \right)$

A) $- 7 n ^ { 2 } + 2 n - 15$
B) $- 7 n ^ { 2 } + 15$
C) $- 7 n ^ { 2 } - 15$
D) $- 7 n ^ { 2 } + 2 n + 15$

Question 32

Subtract the sum of 2 p + 20 and 8 p +7 from 7 p + 2.

A) $- 1 p - 29$
B) $- 3 p + 25$
C) $- 3 p - 25$
D) $- 1 p - 20$

Question 33

Find a polynomial that represents the perimeter of the rectangle in the picture, if a = 4, b = 2 and c = 7.

A) $5 x - 18$
B) $10 x - 18$
C) $10 x + 18$
D) $180 x$
E) $20 x + 36$

Question 34

Subtract the sum of 10 x + 16 and 4 x + 10 from 7 x + 6.

A) $-$ x $-$ 29
B) $-$ x $-$ 16
C) $-$ 7 x + 20
D) $-$ 7 x $-$ 20
E) 7 x + 20

Question 35

Find a polynomial that represents the perimeter of the rectangle with the sides 6 x + 10 and x + 2.

A) $4 x ^ { 2 } - 24$
B) $14 x + 24$
C) $8 x + 48$
D) $120 x$

Question 36

Perform the indicated operations. $10 p - [ 10 p - ( 6 p - 9 ) ]$

A) $6 p - 10$
B) $- 6 p - 9$
C) $6 p - 9$
D) $7 p - 9$
E) $6 p + 9$

Question 37

Subtract the polynomials using a vertical format. $- 2 p - 4 \text { from } 4 p + 11$

A) $- 6 p + 15$
B) $- 6 p - 15$
C) $6 p + 15$
D) $6 p - 15$

Question 38

Find a polynomial that represents the perimeter of the rectangle in the picture, if a = 10, b = 4 and c = 6.

A) $22 x + 20$
B) $44 x + 40$
C) $22 x - 20$
D) $440 x$

Question 39

Perform the indicated operations. $\left( x ^ { 2 } - 4 x - 8 \right) + \left( 8 x ^ { 2 } - 7 x - 6 \right) - \left( 5 x ^ { 2 } - 4 x - 6 \right)$

A) $- 4 x ^ { 2 } - 7 x + 8$
B) $4 x ^ { 2 } + 7 x - 8$
C) $4 x ^ { 2 } - 7 x + 8$
D) $4 x ^ { 2 } - 7 x - 8$

Question 40

Subtract the polynomials using a horizontal format. $8 x ^ { 4 } - 10 x ^ { 2 } + 2 \text { from } 10 x ^ { 4 } + 4 x ^ { 2 } + 9$

A) $- 2 x ^ { 4 } - 14 x ^ { 2 } - 7$
B) $18 x ^ { 4 } + 14 x ^ { 2 } + 7$
C) $2 x ^ { 4 } + 14 x ^ { 2 } + 7$
D) $- 2 x ^ { 4 } + 14 x ^ { 2 } + 7$
E) $2 x ^ { 4 } + 14 x ^ { 2 } - 7$

Question 41

Subtract the sum of 6 x + 17 and 8 x + 7 from 7 x + 11.

Question 42

Add the polynomials.

Question 43

Determine the degree of the polynomial. degree = __________

Question 44

Add the polynomials.

Question 45

Subtract the polynomials using a vertical format.

Question 46

Perform the indicated operations.

Question 47

Determine the degree of the polynomial.

Question 48

Subtract the polynomials using a horizontal format.

Question 49

Determine the degree of the polynomial.

Question 50

Subtract the polynomials using a vertical format.

Question 51

Subtract the sum of 6 z + 5 and 8 z + 3 from 9 z + 3.

Question 52

Add the polynomials.

Question 53

Subtract the polynomials using a horizontal format.

Question 54

Subtract the polynomials using a horizontal format.

Question 55

Add the polynomials.

Question 56

Add the polynomials.

Question 57

Perform the indicated operations.

Question 58

Subtract the polynomials using a vertical format.

Question 59

Subtract the polynomials using a horizontal format.

Question 60

Subtract the polynomials using a horizontal format.

Question 61

Multiply the following. (3 x )(2 x )

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

Question 62

Terms must be similar in order to multiply monomials.

Question 63

Multiply the following. $\left( - 9 x ^ { 5 } b ^ { 5 } \right) ( 8 x b )$

A) $- 69 x ^ { 6 } b ^ { 6 }$
B) $- 74 x ^ { 6 } b ^ { 5 }$
C) $- 72 x ^ { 5 } b ^ { 6 }$
D) $- 72 x ^ { 6 } b ^ { 6 }$

Question 64

When raising a monomial to a power, raise each factor to that power.

Question 65

Find a polynomial that represents the perimeter of the rectangle in the picture, if a = 12, b = 3 and c = 7.

Question 66

Perform the indicated operations.

Question 67

Multiply the following. $\left( 7 x ^ { 2 } \right) ( 9 x ) \left( 8 x ^ { 3 } \right)$

A) $509 x ^ { 5 }$
B) $504 x ^ { 6 }$
C) $504 x ^ { 5 }$
D) $499 x ^ { 5 }$
E) $507 x ^ { 6 }$

Question 68

Perform the indicated operations.

Question 69

Match the corresponding statements.

- $8 x + 26$

A) area of the square with the side 4 x
B) perimeter of the rectangle with the sides 3 x + 9 and x + 4

Question 70

Match the corresponding statements.

- $16 x ^ { 2 }$

A) area of the square with the side 4 x
B) perimeter of the rectangle with the sides 3 x + 9 and x + 4

Question 71

Multiply the following. ( $-$ 6 ab )(7 ab )

A) $- 41 a b$
B) $- 42 a ^ { 2 } b ^ { 2 }$
C) $- 42 a ^ { 2 } b$
D) $- 41 a b ^ { 2 }$

Question 72

Multiply the following. $( 3 c d ) \left( - 6 c ^ { 3 } d \right) ( - 5 d )$

A) $- 89 c ^ { 4 } d ^ { 3 }$
B) $90 c ^ { 3 } d$
C) $87 c ^ { 4 } d ^ { 2 }$
D) $- 90 c ^ { 3 } d ^ { 3 }$
E) $90 c ^ { 4 } d ^ { 3 }$

Question 73

Perform the indicated operations.

Question 74

Multiply the following. $\left( - 6 a b ^ { 3 } c \right) \left( 14 a ^ { 5 } c \right)$

A) $- 84 a ^ { 5 } b ^ { 4 } c ^ { 2 }$
B) $- 84 a ^ { 6 } b ^ { 3 } c$
C) $- 84 a ^ { 6 } b ^ { 3 } c ^ { 2 }$
D) $- 84 a ^ { 6 } b ^ { 4 } c ^ { 2 }$

Question 75

Perform the indicated operations.

Question 76

Perform the indicated operations.

Question 77

Perform the indicated operations.

Question 78

When raising a power to a power, add exponents.

Question 79

The distributive property along with the properties of exonents form a basis for finding the product of a monomial and a polynomial.

Question 80

Multiply the following. $$\left( \frac { 2 } { 3 } x y \right) \left( \frac { 3 } { 5 } x ^ { 2 } y ^ { 2 } \right)$$

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