Deck 5: Polynomials and Polynomial Functions

Question 1

Simplify the polynomial by combining like terms.
$$4 x + 4 x ^ { 3 } + 8 x ^ { 3 } + 9 x$$

A) $12 x ^ { 3 } + 13 x$
B) $25 \mathrm { x } ^ { 3 }$
C) $4 x + 4 x ^ { 3 } + 8 x ^ { 3 } + 9 x$
D) $25 x$

Answer 1

A

Question 2

Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of
these.
9

A) monomial of degree 1
B) monomial of degree 0
C) binomial of degree 0
D) binomial of degree 1

Answer 2

B

Question 3

10

A) 0
B) 10
C) 1
D) no degree

Answer 3

A

Question 4

Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of
these.
$$4 \mathrm { z } ^ { 2 } + \mathrm { z }$$

A) trinomial of degree 2
B) binomial of degree 2
C) binomial of degree 4
D) binomial of degree 1

Question 5

Simplify the polynomial by combining like terms.
$$- 5 x ^ { 2 } + 4 x + 3 x + 5 x$$

A) $- 300 x ^ { 5 }$
B) $- 5 x ^ { 2 } + 7 x$
C) $- 5 x ^ { 2 } + 7 x + 5$
D) $- 5 x ^ { 2 } + 12 x$

Question 6

Find the degree of the term.
$4.61 x ^ { 4 } z ^ { 6 }$

A) 4
B) 6
C) 10
D) no degree

Question 7

Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of
these.
$$13 x ^ { 4 } + 7 x ^ { 3 } - 6 x - 3 y ^ { 5 }$$

A) trinomial of degree 4
B) degree 5 ; none of these
C) degree 4 ; none of these
D) trinomial of degree 5

Question 8

Find the degree of the term.
$- 3 ^ { 5 } y ^ { 2 }$

A) 5
B) 2
C) 7
D) no degree

Question 9

Simplify the polynomial by combining like terms.
$13 y ^ { 2 } + 6 y ^ { 2 }$

A) $19 y ^ { 4 }$
B) $19 y ^ { 2 }$
C) $13 y ^ { 2 } + 6 y ^ { 2 }$
D) $7 y ^ { 2 }$

Question 10

Simplify the polynomial by combining like terms.
$$- 15 x ^ { 9 } + 4 x ^ { 6 } + x ^ { 9 } + 6 x ^ { 9 }$$

A) $- 4 x 18$
B) $- 8 x ^ { 9 } + 4 x ^ { 6 }$
C) $- 4 x ^ { 9 } - 4 x ^ { 6 }$
D) $- 15 x ^ { 9 } + 4 x ^ { 6 } + x ^ { 9 } + 6 x ^ { 9 }$

Question 11

Find the degree of the term.
$- 5 x ^ { 4 }$

A) 1
B) -5
C) 4
D) no degree

Question 12

Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of
these.
$$9 x ^ { 3 } + 16 x ^ { 4 } + 9 x ^ { 2 } + 9$$

A) trinomial of degree 4
B) degree 4 ; none of these
C) degree 3 ; none of these
D) trinomial of degree 3

Question 13

13x

A) 1
B) 13
C) 0
D) no degree

Question 14

Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of
these.
$$- 7 x ^ { 9 } + 8 x - 7$$

A) trinomial of degree 10
B) trinomial of degree 9
C) binomial of degree 10
D) binomial of degree 9

Question 15

Simplify the polynomial by combining like terms.
$7 x ^ { 8 } + 9 x ^ { 6 } + 7 x ^ { 8 }$

A) $14 x ^ { 8 } + 9 x ^ { 6 }$
B) $23 x ^ { 22 }$
C) $23 x^ { 6 }$
D) cannot be simplified

Question 16

Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of
these.
$$- 5 x + 2$$

A) binomial of degree 0
B) binomial of degree 2
C) monomial of degree 1
D) binomial of degree 1

Question 17

Simplify the polynomial by combining like terms.
$$- 9 x y + 8 y ^ { 2 } - 2 x y + 8 x ^ { 2 }$$

A) $- 11 x y + 64 x ^ { 2 } y ^ { 2 }$
B) $18 x y + 64 x ^ { 2 } y ^ { 2 }$
C) $8 x ^ { 2 } - 11 x y + 8 y ^ { 2 }$
D) $5 x ^ { 2 } + 5 x y + 5 y ^ { 2 }$

Question 18

Find the degree of the term.
$- 5 x y ^ { 7 }$

A) -5
B) 8
C) 7
D) no degree

Question 19

Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of
these.
$$6 x ^ { 4 } - 8 x ^ { 4 } y - 5$$

A) degree 4 ; none of these
B) trinomial of degree 4
C) trinomial of degree 5
D) trinomial of degree 9

Question 20

Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of
these.
$- 8 x y ^ { 2 }$

A) binomial of degree 3
B) trinomial of degree 3
C) monomial of degree 2
D) monomial of degree 3

Question 21

Perform the indicated operations and simplify.
$$\begin{array} { r } 5 x ^ { 5 } - 9 x ^ { 4 } + 2 x ^ { 3 } + 3 \\+ \left( 4 x ^ { 5 } - 9 x ^ { 4 } - 8 x ^ { 3 } + 6 \right) \\\hline\end{array}$$

A) $9 x ^ { 5 } - 18 x ^ { 4 } - 6 x ^ { 3 } + 9$
B) $- 15 x ^ { 24 } + 9$
C) $- 6 x ^ { 5 } - 6 x ^ { 4 } + 11 x ^ { 3 } - 5$
D) $9 x ^ { 10 } - 18 x ^ { 8 } - 6 x ^ { 6 } + 9$

Question 22

Perform the indicated operations and simplify.
$$\left( - 6 x ^ { 2 } y - x y \right) + \left( 8 x ^ { 2 } y + 3 x y \right)$$

A) $2 x ^ { 2 } y + 4 x y$
B) $14 x ^ { 2 } y + 2 x y$
C) $14 x ^ { 2 } y + 4 x y$
D) $2 x ^ { 2 } y + 2 x y$

Question 23

Perform the indicated operations and simplify.
$$\left( 7 x ^ { 4 } + 7 x ^ { 3 } - 2 x ^ { 2 } - 2 \right) + \left( 3 x ^ { 4 } - 2 x ^ { 3 } - 6 x ^ { 2 } - 9 \right)$$

A) $10 x ^ { 4 } + 5 x ^ { 3 } - 2 x ^ { 2 } + 10$
B) $10 x ^ { 4 } + 5 x ^ { 3 } - 8 x ^ { 2 } - 11$
C) $7 x ^ { 18 } - 11$
D) $10 x ^ { 8 } + 5 x ^ { 6 } - 8 x ^ { 4 } - 11$

Question 24

Simplify the polynomial by combining like terms.
$\left( 8 x ^ { 2 } - x y - y ^ { 2 } \right)$ and $\left( x ^ { 2 } + 12 x y + 10 y ^ { 2 } \right)$

A) $7 x ^ { 2 } - 13 x y - 11 y ^ { 2 }$
B) $9 x ^ { 2 } + 11 x y + 9 y ^ { 2 }$
C) $9 x ^ { 2 } + 13 x y + 11 y ^ { 2 }$
D) $8 x ^ { 2 } + 12 x y + 10 y ^ { 2 }$

Question 25

Perform the indicated operations and simplify.
$\left( 7 y ^ { 2 n } - 4 y ^ { n } + 2 \right) + \left( 4 y ^ { 2 n } + 2 y ^ { n } - 4 \right)$

A) $6 y ^ { 2 n } + 9 y ^ { n } - 8$
B) $7 y ^ { 3 n }$
C) $11 y ^ { 4 n } - 2 y ^ { 2 n } - 2$
D) $11 y ^ { 2 n } - 2 y ^ { n } - 2$

Question 26

Simplify the polynomial by combining like terms.
$$\left( 7 x ^ { 6 } + 9 x ^ { 5 } + 4 x \right) + \left( 4 x ^ { 6 } - 3 x ^ { 5 } + 5 x \right)$$

A) $11 x ^ { 6 } + 6 x ^ { 5 } + 9 x$
B) $26 \mathrm { x } ^ { 12 }$
C) $8 x ^ { 6 } + 4 x ^ { 5 } + 14 x$
D) $11 x + 6 x ^ { 6 } + 9 x ^ { 5 }$

Question 27

Perform the indicated operations and simplify.
$$\left( 8 x ^ { 5 } + 9 x ^ { 4 } \right) + \left( 5 x ^ { 5 } - 3 x ^ { 4 } \right)$$

A) $19 x ^ { 9 }$
B) $13 x ^ { 10 } + 6 x ^ { 8 }$
C) $13 x ^ { 5 } + 6 x ^ { 4 }$
D) $19 x ^ { 18 }$

Question 28

Perform the indicated operations and simplify.
$$\begin{array} { r } 8 x ^ { 7 } + 4 x ^ { 6 } + 4 x \\+ \left( 2 x ^ { 7 } + 4 x ^ { 6 } + 2 x \right) \\\hline\end{array}$$

A) $10 x + 8 x ^ { 7 } + 6 x ^ { 6 }$
B) $24 \mathrm { x } ^ { 14 }$
C) $6 x ^ { 7 } + 12 x ^ { 6 } + 6 x$
D) $10 x ^ { 7 } + 8 x ^ { 6 } + 6 x$

Question 29

Simplify the polynomial by combining like terms.
$$\begin{array} { r } 3 x ^ { 5 } + 5 x ^ { 2 } + 5 \\+ \left( 6 x ^ { 5 } - 9 x ^ { 2 } - 7 \right) \\\hline\end{array}$$

A) $11 x ^ { 5 } - 6 x ^ { 2 } - 2$
B) $9 - 4 x ^ { 5 } - 2 x ^ { 2 }$
C) $3 x ^ { 7 }$
D) $9 x ^ { 5 } - 4 x ^ { 2 } - 2$

Question 30

Simplify the polynomial by combining like terms.
$$\left( \frac { 2 } { 5 } x ^ { 2 } + \frac { 2 } { 5 } x + \frac { 3 } { 4 } \right) + \left( \frac { 4 } { 5 } x ^ { 2 } - \frac { 3 } { 4 } x + \frac { 1 } { 4 } \right)$$

A) $\frac { 6 } { 5 } x ^ { 4 } - \frac { 7 } { 20 } x ^ { 2 } + 1$
B) $\frac { 6 } { 5 } x ^ { 2 } - \frac { 7 } { 20 } x - 1$
C) $\frac { 6 } { 5 } x ^ { 2 } - \frac { 7 } { 20 } x + 1$
D) $\frac { 17 } { 20 } x ^ { 6 } + 1$

Question 31

Simplify the polynomial by combining like terms.
$$\begin{array} { r } 5 x ^ { 5 } + 5 x ^ { 2 } \\+ \left( 2 x ^ { 5 } - 8 x ^ { 2 } \right) \\\hline\end{array}$$

A) $7 x ^ { 10 } - 3 x ^ { 4 }$
B) $4 x ^ { 14 }$
C) $7 x ^ { 5 } - 3 x ^ { 2 }$
D) $4 \mathrm { x } ^ { 7 }$

Question 32

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

A) $8 x ^ { 2 n } + 9 x ^ { n } + 5$
B) $9 x ^ { 2 n } + 8 x ^ { n } + 4$
C) $9 x ^ { 4 n } + 10 x ^ { 2 n } + 6$
D) $7 x ^ { 4 n } - 10 x ^ { 2 n } - 6$

Question 33

Perform the indicated operations and simplify.
$$( 2 x - 8 ) + ( 8 x + 10 )$$

A) $10 x + 2$
B) $10 x ^ { 2 } + 2$
C) $10 x - 2$
D) $16 \mathrm { x } ^ { 2 } - 80$

Question 34

Perform the indicated operations and simplify.
$\left( 6 x ^ { 6 } + 5 x ^ { 3 } \right) + \left( 9 x ^ { 6 } + 6 x ^ { 3 } + 4 \right)$

A) $39 x ^ {10 }$
B) $18 x ^ { 6 } + 12 x ^ { 3 } + 4 x$
C) $4 x + 11 x ^ { 6 } + 13 x ^ { 3 }$
D) $15 x ^ { 6 } + 11 x ^ { 3 } + 4$

Question 35

Simplify the polynomial by combining like terms.
$$\left( 5 x ^ { 5 } y ^ { 3 } + 10 x ^ { 3 } y ^ { 2 } + 6 x y \right) + \left( 3 x ^ { 5 } y ^ { 3 } + 11 x ^ { 3 } y + 12 x y \right)$$

A) $8 x ^ { 5 } y ^ { 3 } + 21 x ^ { 3 } y ^ { 2 } + 18 x y$
B) $8 x ^ { 5 } y ^ { 3 } + 10 x ^ { 3 } y ^ { 2 } + 11 x ^ { 3 } y + 18 x y$
C) $8 x ^ { 5 } y ^ { 3 } + 21 x ^ { 3 } y + 18 x y$
D) $21 x ^ { 6 } y ^ { 3 } + 8 x ^ { 5 } y ^ { 3 } + 18 x y$

Question 36

Simplify the polynomial by combining like terms.
$$- 11 x ^ { 9 } - 8 x ^ { 3 } y - 3 x ^ { 9 } - \frac { 1 } { 9 } - 1 x ^ { 3 } y - 4 x ^ { 9 }$$

A) $- 18 x ^ { 9 } - 9 x ^ { 3 } y - \frac { 1 } { 9 }$
B) $- 27 x ^ { 9 } - \frac { 1 } { 9 }$
C) $- 18 x ^ { 9 } - 8 x ^ { 3 } y - \frac { 1 } { 9 }$
D) $- 27 x ^ { 9 } - 27 x ^ { 3 } y - \frac { 1 } { 9 }$

Question 37

Find the perimeter.

A) $\left( x ^ { 2 } + 8 x + 4 \right)$ units
B) $\left( x ^ { 4 } + 8 x ^ { 2 } + 4 \right)$ units
C) $\left( 4 x ^ { 2 } + 16 x + 8 \right)$ units
D) $\left( x ^ { 4 } + 16 x ^ { 2 } + 8 \right)$ units

Question 38

Find the perimeter.

A) $\left( 2 x ^ { 2 } + 16 x + 44 \right)$ units
B) $\left( x ^ { 2 } + 6 x + 22 \right)$ units
C) $\left( 2 x ^ { 2 } + 12 x + 22 \right)$ units
D) $\left( 2 x ^ { 2 } + 12 x + 44 \right)$ units

Question 39

Simplify the polynomial by combining like terms.
$$\left( 12 x ^ { 2 } y - 9 x y + 7 \right) + \left( - 11 x ^ { 2 } y + 5 x y - 8 \right)$$

A) $23 x ^ { 2 } y + 14 x y + 15$
B) $- x ^ { 2 } y - 14 x y + 15$
C) $- 4 x ^ { 3 } y ^ { 2 } - 1$
D) $x ^ { 2 } y - 4 x y - 1$

Question 40

Simplify the polynomial by combining like terms.
$$3 x ^ { 9 } + 11 x ^ { 4 } + 13 x ^ { 9 } + 3 x ^ { 9 } - 1 x ^ { 4 }$$

A) $19 x ^ { 9 } + 10 x ^ { 4 }$
B) $29 \mathrm { x } ^ { 9 }$
C) $3 x ^ { 9 } + 11 x ^ { 4 } + 13 x ^ { 9 } + 3 x ^ { 9 } - 1 x ^ { 4 }$
D) $29 x ^ { 9 } + 29 x ^ { 4 }$

Question 41

Subtract.
$\left( 2.6 x ^ { 3 } - 6.2 x ^ { 2 } - 1 \right) - \left( 8.5 x ^ { 3 } - 2.4 x ^ { 2 } + 3 \right)$

A) $11.1 x ^ { 3 } - 3.8 x ^ { 2 } - 4$
B) $- 5.9 x ^ { 3 } - 3.8 x ^ { 2 } + 4$
C) $- 5.9 x ^ { 3 } - 8.6 x ^ { 2 } - 4$
D) $- 5.9 x ^ { 3 } - 3.8 x ^ { 2 } - 4$

Question 42

Subtract.
Subtract $( 3 x - 30 )$ from the sum of $( - 2 x + 12 )$ and $( 9 x - 1 )$ .

A) $4 x + 41$
B) $10 x - 19$
C) $- 4 x - 41$
D) $8 x + 43$

Question 43

Find the function value.
If $P ( x ) = 9 x - 7$ , find $P ( - 5 )$ .

A) 52
B) 38
C) $- 38$
D) $- 52$

Question 44

Subtract.
$$\left( 3 x ^ { 7 } + 7 x ^ { 6 } + 5 \right) - \left( 6 x ^ { 7 } + 19 x ^ { 6 } + 14 \right)$$

A) $- 3 x ^ { 7 } - 12 x ^ { 6 } + 19$
B) $- 24 x ^ { 13 }$
C) $- 3 x ^ { 7 } + 13 x ^ { 6 } + 19$
D) $- 3 x ^ { 7 } - 12 x ^ { 6 } - 9$

Question 45

Subtract.
Subtract $( x + 5 )$ from $( 8 x + 7 )$

A) $8 x + 12$
B) $7 x + 12$
C) $8 x + 2$
D) $7 x + 2$

Question 46

Subtract.
$$\begin{array} { r } 5 x ^ { 8 } + 4 x ^ { 7 } + 5 x ^ { 6 } - 6 \\- \left( 3 x ^ { 8 } + 9 x ^ { 7 } - 7 x ^ { 6 } - 2 \right) \\\hline\end{array}$$

A) $2 x ^ { 8 } - 5 x ^ { 7 } + 12 x ^ { 6 } - 4$
B) $8 x ^ { 8 } + 13 x ^ { 7 } - 2 x ^ { 6 } - 4$
C) $8 x ^ { 8 } + 13 x ^ { 7 } - 2 x ^ { 6 } - 8$
D) $2 x ^ { 8 } + 13 x ^ { 7 } - 2 x ^ { 6 } - 8$

Question 47

Subtract.
$$\left( 3 x ^ { 9 } - 2 x ^ { 8 } + 9 x ^ { 7 } + 4 \right) - \left( 8 x ^ { 9 } + 4 x ^ { 8 } + 5 x ^ { 7 } + 8 \right)$$

A) $- 5 x ^ { 9 } - 6 x ^ { 8 } + 4 x ^ { 7 } - 4$
B) $- 5 x ^ { 9 } + 2 x ^ { 8 } + 14 x ^ { 7 } + 12$
C) $11 x ^ { 9 } + 2 x ^ { 8 } + 14 x ^ { 7 } + 12$
D) $11 x ^ { 9 } + 2 x ^ { 8 } + 14 x ^ { 7 } - 4$

Question 48

Subtract.
$$\left( 3 y ^ { 2 n } + 6 y ^ { n } - 1 \right) - \left( 4 y ^ { 2 n } + 3 y ^ { n } + 6 \right)$$

A) $- y ^ { 2 n } + 3 y ^ { n } + 5$
B) $y ^ { 2 n } + 3 y ^ { n } - 7$
C) $- y ^ { 2 n } - 3 y ^ { n } - 7$
D) $- y ^ { 2 n } + 3 y ^ { n } - 7$

Question 49

Subtract.
Subtract $\left( 3.5 x ^ { 2 } - x - 9.4 \right)$ from the sum of $\left( 1.7 x ^ { 3 } + 7.8 x ^ { 2 } + 4.7 \right)$ and $( 6.9 x - 2.8 )$ .

A) $1.7 x ^ { 3 } + 4.3 x ^ { 2 } + 6.9 x + 11.3$
B) $13.9 x ^ { 6 } + 11.3$
C) $1.7 x ^ { 3 } + 4.3 x ^ { 2 } + 7.9 x + 11.3$
D) $1.7 x ^ { 3 } + 11.3 x ^ { 2 } + 5.9 x - 7.5$

Question 50

Find the perimeter.

A) $\left( 4 x ^ { 2 } + 8 x + 31 \right)$ units
B) $\left( 4 x ^ { 2 } + 8 x + 20 \right)$ units
C) $\left( 4 x ^ { 2 } + 2 x + 31 \right)$ units
D) $\left( 3 x ^ { 2 } + 2 x + 20 \right)$ units

Question 51

Subtract.
$$\left( x ^ { 3 } + 9 x y - 4 y ^ { 2 } \right) - \left( 6 x ^ { 3 } + 4 x y + y ^ { 2 } \right)$$

A) $7 x ^ { 3 } + 5 x y - 5 y ^ { 2 }$
B) $5 x ^ { 3 } - 5 x y - 3 y ^ { 2 }$
C) $- 5 x ^ { 3 } + 5 x y - 3 y ^ { 2 }$
D) $- 5 x ^ { 3 } + 5 x y - 5 y ^ { 2 }$

Question 52

Subtract.
$$\left( 6 x ^ { 3 } + 2 x y ^ { 2 } + 8 y ^ { 3 } \right) - \left( 4 x ^ { 3 } + 12 x ^ { 2 } y + 9 x y ^ { 2 } + 5 y ^ { 3 } \right)$$

A) $- 2 x ^ { 3 } + 12 x ^ { 2 } y + 7 x y ^ { 2 } - 3 y ^ { 3 }$
B) $2 x ^ { 3 } + 12 x ^ { 2 } y - 7 x y ^ { 2 } + 3 y ^ { 3 }$
C) $10 x ^ { 3 } + 12 x ^ { 2 } y + 15 x y ^ { 2 } + 13 y ^ { 3 }$
D) $2 x ^ { 3 } - 12 x ^ { 2 } y - 7 x y ^ { 2 } + 3 y ^ { 3 }$

Question 53

Find the function value.
If $Q ( x ) = - 4 x ^ { 2 } - 9 x - 2$ , find $Q ( - 3 )$

A) $- 65$
B) $- 11$
C) 7
D) 61

Question 54

Subtract.
$$( 4 x + 9 ) - ( - x - 1 )$$

A) $4 x + 8$
B) $3 x + 8$
C) $5 x + 8$
D) $5 x + 10$

Question 55

Subtract.
$$\begin{array} { r } 6 n ^ { 6 } + 6 n ^ { 3 } + 18 \\- \left( 4 n ^ { 6 } - 14 n ^ { 3 } - 13 \right) \\\hline\end{array}$$

A) $2 n ^ { 6 } + 20 n ^ { 3 } + 5$
B) $2 n ^ { 6 } + 20 n ^ { 3 } + 31$
C) $53 n ^ { 9 }$
D) $2 n ^ { 6 } + 10 n ^ { 3 } + 5$

Question 56

Subtract.
$$\left( 5 x ^ { 2 } + 9 x - 4 \right) - \left( - 10 x ^ { 2 } - 3 \right)$$

A) $- 5 x ^ { 2 } + 9 x - 1$
B) $15 x ^ { 2 } + 12 x - 4$
C) $- 5 x ^ { 2 } + 12 x - 4$
D) $15 x ^ { 2 } + 9 x - 1$

Question 57

Subtract.
$$\left( - 9 a ^ { 2 } b ^ { 4 } + 3 a b ^ { 2 } + 4 a b \right) - \left( 7 a ^ { 2 } b ^ { 4 } + 5 a b ^ { 2 } - a b \right)$$

A) $16 a ^ { 2 } b ^ { 4 } + 2 a b ^ { 2 } - 5 a b$
B) $- 16 a ^ { 2 } b ^ { 4 } - 2 a b ^ { 2 } + 5 a b$
C) $- 16 a ^ { 2 } b ^ { 4 } + 2 a b ^ { 2 } + 3 a b$
D) $- 2 a ^ { 2 } b ^ { 4 } + 8 a b ^ { 2 } + 3 a b$

Question 58

Subtract.
$$\begin{array} { r } x ^ { 4 } + 8 x ^ { 3 } \\- \left( 15 x ^ { 4 } + 13 x ^ { 3 } \right) \\\hline\end{array}$$

A) $- 14 x ^ { 4 } - 5 x ^ { 3 }$
B) $34 x ^ { 4 } + 21 x ^ { 3 }$
C) $- 14 x ^ { 4 } + 21 x ^ { 3 }$
D) $- 19 x ^ { 7 }$

Question 59

Subtract.
$$\left( 8 x ^ { 2 n } + 13 x ^ { n } + 7 \right) - \left( 4 x ^ { 2 n } + 9 x ^ { n } + 13 \right)$$

A) $4 x ^ { 2 n } + 17 x ^ { n } + 20$
B) $4 x ^ { 2 n } + 4 x ^ { n } + 20$
C) $4 x ^ { 2 n } + 4 x ^ { n } - 6$
D) $4 x ^ { 4 n } + 4 x ^ { 2 n } - 6$

Question 60

Subtract.
$$\left( 8 x ^ { 7 } + 8 x ^ { 5 } - 16 \right) - \left( - 18 x ^ { 5 } + 4 x ^ { 7 } + 16 \right)$$

A) $4 x ^ { 7 } + 26 x ^ { 5 } - 32$
B) $- 2 x ^ { 12 }$
C) $4 x ^ { 7 } + 12 x ^ { 5 } - 32$
D) $4 x ^ { 7 } + 26 x ^ { 5 } + 32$

Question 61

Find the function.
If $P ( x ) = 6 x - 8$ , find $P ( - x )$ .

A) $2 x$
B) $6 x + 8$
C) $- 6 x - 8$
D) $- 6 x + 8$

Question 62

Multiply.
$12 x y ( 3 x - 10 y )$

A) $36 x ^ { 2 } y - 120 x y ^ { 2 }$
B) $15 x ^ { 2 } - 22 y ^ { 2 }$
C) $15 x ^ { 2 } y - 22 x y ^ { 2 }$
D) $36 x ^ { 2 } - 120 y ^ { 2 }$

Question 63

Multiply.
$- 2 x ^ { 2 } y \left( - 3 x ^ { 2 } y ^ { 4 } - 6 x y ^ { 3 } + 10 \right)$

A) $6 x ^ { 4 } y ^ { 5 } + 12 x ^ { 3 } y ^ { 4 } - 20 x ^ { 2 } y$
B) $6 x ^ { 4 } y ^ { 5 } - 12 x ^ { 3 } y ^ { 4 } + 20 x ^ { 2 } y$
C) $6 x ^ { 4 } y ^ { 5 } + 12 x ^ { 3 } y ^ { 4 } - 20$
D) $6 x ^ { 2 } y ^ { 5 } + 12 x ^ { 3 } y ^ { 4 } - 20 x ^ { 2 } y$

Question 64

Find the function value.
If $P ( x ) = 5 x ^ { 2 } - 9 x$ , find $P ( - 2 )$ .

A) 8
B) 20
C) 9
D) 38

Question 65

Solve.
The total cost (in dollars) for a certain company to produce $x$ glass jars per week is given by the polynomial function $\mathrm { C } ( \mathrm { x } ) = 0.4 \mathrm { x } + 40,000$ . Find the total cost of producing 80,000 jars per week.

A) $\$ 80,040$
B) $\$ 72,000$
C) $\$ 32,000$
D) $\$ 40.40$

Question 66

Multiply.
$$\left( 5 x ^ { 2 } \right) \left( - 2 x ^ { 3 } \right)$$

A) $- 10 x ^ { 6 }$
B) $10 x ^ { 6 }$
C) $- 10 x ^ { 5 }$
D) $10 x ^ { 5 }$

Question 67

Multiply.
$\left( 5.8 \mathrm { x } ^ { 5 } \mathrm { y } ^ { 2 } \mathrm { z } \right) \left( 10 \mathrm { x } ^ { 3 } \mathrm { y } ^ { 5 } \mathrm { z } ^ { 9 } \right)$

A) $58 x ^ { 8 } y ^ { 7 } z ^ { 10 }$
B) $580 \mathrm { x } 1 \mathrm { y } _ { \mathrm { y } } 10 _ { \mathrm { z } } \mathrm { 9 }$
C) $58 \mathrm { x } ^ { 15 } \mathrm { y } ^ { 10 } \mathrm { z } 9$
D) $5.8 \mathrm { x } ^ { 8 } \mathrm { y } ^ { 7 } \mathrm { z } ^ { 10 }$

Question 68

Find the function value.
If $P ( x ) = x ^ { 2 } + 7 x - 4$ , find $P ( 4 )$

A) 40
B) 28
C) 19
D) 44

Question 69

Solve.
A object is thrown upward with an initial velocity of 21 feet per second from the top of a 572 -foot building. The height of the object above the ground at any time $t$ can be described by the polynomial function $P ( t ) = - 16 t ^ { 2 } + 21 t + 572$ . Find the height of the object at $t = 4$ seconds.

A) $400 \mathrm { ft }$
B) $592 \mathrm { ft }$
C) $572 \mathrm { ft }$
D) $337 \mathrm { ft }$

Question 70

Find the function value.
If $Q ( x ) = 3 x ^ { 2 } - 5 x - 3$ , find $Q ( 0 )$

A) $- 5$
B) 3
C) 0
D) $- 3$

Question 71

Multiply.
$12 x ( 6 x - 10 )$

A) $72 x ^ { 2 } - 120 x$
B) $72 x ^ { 2 }$
C) $6 x ^ { 2 } - 120 x$
D) $72 x ^ { 2 } + 12 x$

Question 72

Solve.
A projectile is fired upward from the ground with an initial velocity of 200 feet per second. Neglecting air resistance, the height of the projectile at any time $t$ can be described by the polynomial function $P ( t ) = - 16 t ^ { 2 } +$ $200 \mathrm { t }$ . Find the height of the projectile at $\mathrm { t } = 4$ seconds.

A) $644 \mathrm { ft }$
B) $544 \mathrm { ft }$
C) $736 \mathrm { ft }$
D) $800 \mathrm { ft }$

Question 73

Find the function.
If $P ( x ) = 5 x + 8$ , find $P ( a )$

A) $13 a$
B) $5 a$
C) $5 x + 8$
D) $5 a + 8$

Question 74

Find the function value.
If $Q ( x ) = x ^ { 2 } - 5$ , find $Q ( - 1 )$ .

A) 36
B) 1
C) $- 6$
D) $- 4$

Question 75

Find the function.
If $P ( x ) = 5 x + 2$ , find $P ( x + h )$

A) $5 x + h + 2$
B) $5 x + 5 h + 2 h$
C) $5 x + 5 h + 2$
D) $x + h + 2$

Question 76

Multiply.
$12 a b ^ { 2 } \left( 11 a ^ { 2 } b ^ { 3 } + 3 a b \right)$

A) $132 a ^ { 2 } b ^ { 5 } + 36 a ^ { 2 } b ^ { 3 }$
B) $132 a ^ { 3 } b ^ { 5 } + 36 a ^ { 2 } b ^ { 3 }$
C) $132 a ^ { 3 } b ^ { 4 } + 36 a ^ { 2 } b ^ { 3 }$
D) $132 a ^ { 3 } b ^ { 5 } + 36 a ^ { 2 } b ^ { 2 }$

Question 77

Solve.
The polynomial function $\mathrm { P } ( x ) = 0.95 x - 84$ models the relationship between the number of pretzels $x$ that a certain vendor sells and the profit the vendor makes, $\mathrm { P } ( \mathrm { x } )$ . Find $\mathrm { P } ( 800 )$ , the profit the vendor makes from selling 800 pretzels.

A) $- \$ 74.50$
B) $\$ 716$
C) $\$ 676$
D) $\$ 760$

Question 78

Solve.
The function $f ( x ) = 0.054 x ^ { 2 } + 0.66 x + 4.5$ can be used to approximate the number of computers sold during the years $1990 - 2000$ , where $x$ is the number of years after 1990 and $f ( x )$ is the number of computers sold (in millions). Approximate the number of computers sold in 1998. Round your answer to the nearest tenth of a million.

A) $11.8$ million
B) $13.2$ million
C) $4.5$ million
D) $10.2$ million

Question 79

Find the function.
If $P ( x ) = 2 x + 5$ and $Q ( x ) = - 3 x ^ { 2 } + 7 x + 5$ , find $P ( x ) + Q ( x )$

A) $- 3 x ^ { 2 } + 9 x - 10$
B) $- 3 x ^ { 2 } + 9 x + 10$
C) $- 3 x ^ { 2 } - 9 x + 10$
D) $3 x ^ { 2 } + 9 x + 10$

Question 80

Solve.
The total revenues (in dollars) for a hot dog vendor selling $x$ hot dogs per day is given by the polynomial function $R ( x ) = 3 x$ . Find the total revenue from selling 60 hot dogs per day.

A) $\$ 18.00$
B) $\$ 1080.00$
C) $\$ 180.00$
D) $\$ 1800.00$