Deck 5: Exponents and Polynomials

Question 1

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial.
$$17 x ^ { 6 } + 7 x - 1$$

A) Trinomial, degree 6
B) Binomial, degree 7
C) Trinomial, degree 7
D) Trinomial, degree 8

Answer 1

Trinomial, degree 6

Question 2

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial.
$$19 y ^ { 9 }$$

A) Binomial, degree 19
B) Binomial, degree 9
C) Monomial, degree 19
D) Monomial, degree 9

Answer 2

Monomial, degree 9

Question 3

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial.
8

A) Monomial, degree 0
B) Monomial, degree 1
C) Monomial, degree 8
D) Binomial, degree 0

Answer 3

Monomial, degree 0

Question 4

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial.
$$- 16 y + 3$$

A) Binomial, degree 0
B) Monomial, degree -16
C) Binomial, degree 2
D) Binomial, degree 1

Question 5

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial.
$$- 13 x ^ { 2 }$$

A) Binomial, degree -13
B) Binomial, degree 0
C) Monomial, degree 2
D) Monomial, degree -13

Question 6

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial.
$$13 y ^ { 3 } + 9 y ^ { 2 } + 3$$

A) Trinomial, degree 3
B) Trinomial, degree 5
C) Trinomial, degree 6
D) Binomial, degree 3

Question 7

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial.
$$5 x ^ { 4 } + 3 x ^ { 3 } - 7 x ^ { 2 }$$

A) Binomial, degree 9
B) Trinomial, degree 9
C) Trinomial, degree 4
D) Binomial, degree 3

Question 8

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial.
-14x

A) Monomial, degree 1
B) Monomial, degree 0
C) Monomial, degree -14
D) Binomial, degree 0

Question 9

Use a vertical format to add the polynomials.
$$\begin{array} { r } 9 y ^ { 5 } + 3 y ^ { 3 } \\3 y ^ { 5 } - 5 y ^ { 3 } \\\hline\end{array}$$

A) $10 y ^ { 8 }$
B) $12 y ^ { 5 } - 2 y ^ { 3 }$
C) $12 y ^ { 10 } - 2 y ^ { 6 }$
D) $10 \mathrm { y } ^ { 16 }$

Question 10

Add the polynomials.
$$\left( 9 x ^ { 3 } + 5 x + 7 \right) + \left( 8 x ^ { 2 } + 4 x + 5 \right)$$

A) $17 x ^ { 3 } + 9 x + 12$
B) $17 x ^ { 3 } + 13 x ^ { 2 } + 7 x + 5$
C) $9 x ^ { 3 } + 13 x ^ { 2 } + 11 x + 5$
D) $9 x ^ { 3 } + 8 x ^ { 2 } + 9 x + 12$

Question 11

Add the polynomials.
$$\left( 7 y ^ { 5 } + 8 y ^ { 3 } \right) + \left( 6 y ^ { 5 } - 4 y ^ { 3 } \right)$$

A) $17 y ^ { 16 }$
B) $13 y ^ { 10 } + 4 y ^ { 6 }$
C) $17 y ^ { 8 }$
D) $13 y ^ { 5 } + 4 y ^ { 3 }$

Question 12

Add the polynomials.
$\left( - \frac { 1 } { 5 } x ^ { 2 } - \frac { 1 } { 4 } x - \frac { 1 } { 4 } \right) + \left( - \frac { 1 } { 3 } x ^ { 2 } - \frac { 1 } { 2 } x - \frac { 1 } { 4 } \right)$

A) $- \frac { 8 } { 15 } x ^ { 4 } - \frac { 3 } { 4 } x ^ { 2 } - \frac { 1 } { 2 }$
B) $- \frac { 77 } { 60 } x ^ { 6 } - \frac { 1 } { 2 }$
C) $\frac { 2 } { 3 } x ^ { 2 } + \frac { 5 } { 4 } x + \frac { 5 } { 8 }$
D) $- \frac { 8 } { 15 } x ^ { 2 } - \frac { 3 } { 4 } x - \frac { 1 } { 2 }$

Question 13

Use a vertical format to add the polynomials.
$$\begin{array} { l } 2 y ^ { 5 } + 9 y ^ { 2 } + 5 \\9 y ^ { 5 } - 4 y ^ { 2 } + 8 \\\hline\end{array}$$

A) $14 y ^ { 5 } - 2 y ^ { 2 } + 17$
B) $11 y ^ { 5 } + 5 y ^ { 2 } + 13$
C) $11 + 5 y ^ { 5 } + 13 y ^ { 2 }$
D) $29 y ^ { 7 }$

Question 14

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial.
$$- 8 y ^ { 6 } + 3$$

A) Monomial, degree -8
B) Binomial, degree 0
C) Binomial, degree 7
D) Binomial, degree 6

Question 15

Use a vertical format to add the polynomials.
$$\begin{array} { r } 9 x ^ { 4 } + 2 x ^ { 3 } \\6 x ^ { 4 } + 7 x ^ { 3 } \\\hline\end{array}$$

A) $15 x ^ { 4 } + 9 x ^ { 3 }$
B) $24 x ^ { 7 }$
C) $15 x ^ { 8 } + 9 x ^ { 6 }$
D) $24 \mathrm { x } ^ { 14 }$

Question 16

Add the polynomials.
$$\left( 2 y ^ { 7 } - 2 y ^ { 5 } - 2 y \right) + \left( 7 y ^ { 7 } - 7 y ^ { 5 } + 5 y \right)$$

A) $5 y ^ { 7 } - 5 y ^ { 5 } + 3 y$
B) $3 y 13$
C) $9 y - 9 y ^ { 7 } + 3 y ^ { 5 }$
D) $9 y ^ { 7 } - 9 y ^ { 5 } + 3 y$

Question 17

Add the polynomials.
$\left( 6 x ^ { 2 } - 3 x + 8 \right) + \left( 3 x ^ { 2 } - 3 x - 2 \right)$

A) $9 x ^ { 4 } - 6 x ^ { 2 } + 6$
B) $9 x ^ { 2 } - 3 x + 6$
C) $18 x ^ { 2 } - 3 x + 6$
D) $9 x ^ { 2 } - 6 x + 6$

Question 18

Use a vertical format to add the polynomials.
$$\begin{array} { l } 5 x ^ { 8 } + 2 x ^ { 7 } - 8 x ^ { 6 } + 6 \\9 x ^ { 8 } + 2 x ^ { 7 } + 6 x ^ { 6 } - 9 \\\hline\end{array}$$

A) $8 x ^ { 8 } + 8 x ^ { 7 } - 4 x ^ { 6 } + 11$
B) $16 x ^ { 42 } - 3$
C) $14 x ^ { 8 } + 4 x ^ { 7 } - 2 x ^ { 6 } - 3$
D) $14 x ^ { 16 } + 4 x ^ { 14 } - 2 x ^ { 12 } - 3$

Question 19

Add the polynomials.
$$( 5 y + 3 ) + ( 2 y + 14 )$$

A) $7 y ^ { 2 } + 17$
B) $7 y + 17$
C) $10 y ^ { 2 } + 42$
D) $7 y - 17$

Question 20

Add the polynomials.
$$\left( 5 x ^ { 6 } + 9 x ^ { 5 } - 3 \right) + \left( 7 x ^ { 6 } + 9 x ^ { 5 } + 4 \right)$$

A) $12 + 18 x ^ { 6 } + 1 x ^ { 5 }$
B) $12 x ^ { 6 } + 18 x ^ { 5 } + 1$
C) $31 \mathrm { x } ^ { 11 }$
D) $4 x ^ { 6 } + 14 x ^ { 5 } + 13$

Question 21

Perform the indicated operations.
$\left[ \left( 1.1 x ^ { 3 } + 7.9 x ^ { 2 } + 4.2 \right) + ( 6.2 x - 2.3 ) \right] - \left( 3.7 x ^ { 2 } - x - 9.9 \right)$

A) $1.1 x ^ { 3 } + 4.2 x ^ { 2 } + 6.2 x + 11.8$
B) $12.5 x ^ { 6 } + 11.8$
C) $1.1 x ^ { 3 } + 11.6 x ^ { 2 } + 5.2 x - 8$
D) $1.1 x ^ { 3 } + 4.2 x ^ { 2 } + 7.2 x + 11.8$

Question 22

Use a vertical format to subtract the polynomials.
$$\begin{array} { r } 0.07 y ^ { 3 } - 0.09 y ^ { 2 } + 0.02 y \\- \left( 0.02 y ^ { 3 } - 0.07 y ^ { 2 } - \quad y \right) \\\hline\end{array}$$

A) $0.5 y ^ { 3 } - 0.16 y ^ { 2 } + 0.03 y$
B) $0.05 \mathrm { y } ^ { 3 } - 0.02 \mathrm { y } ^ { 2 } + 1.02 \mathrm { y }$
C) $0.5 y ^ { 3 } - 0.02 y ^ { 2 } + 0.01 y$
D) $0.05 y ^ { 3 } - 0.16 y ^ { 2 } - 0.98 y$

Question 23

Use a vertical format to subtract the polynomials.
$$\begin{array} { l } 4 x ^ { 4 } - 4 x ^ { 3 } + 7 x ^ { 2 } \\- \left( \quad - x ^ { 3 } - 9 x ^ { 2 } + x - 14 \right) \\\hline\end{array}$$

A) $4 x ^ { 4 } - 3 x ^ { 3 } - 2 x ^ { 2 } + x - 14$
B) $4 x ^ { 4 } - 3 x ^ { 3 } + 16 x ^ { 2 } - x + 14$
C) $4 x ^ { 4 } - 5 x ^ { 3 } + 16 x ^ { 2 } + x - 14$
D) $4 x ^ { 4 } - 5 x ^ { 3 } - 2 x ^ { 2 } - x + 14$

Question 24

Subtract the polynomials.
$\left( y ^ { 6 } - y ^ { 2 } \right) - \left( y ^ { 4 } - y \right)$

A) $y ^ { 6 } - y ^ { 4 } - y ^ { 2 } + y$
B) $y ^ { 6 } - y ^ { 2 } + y ^ { 4 } + y$
C) $y ^ { 6 } - y ^ { 4 } - y ^ { 2 } - y$
D) $y ^ { 6 } - y ^ { 4 } + y ^ { 2 } - y$

Question 25

Use a vertical format to add the polynomials.
$$\begin{array} { r r } - 7 x ^ { 3 } & + 7 x - 6 \\5 x ^ { 2 } & + 8 x - 5 \\\hline\end{array}$$

A) $- 7 x ^ { 3 } + 12 x ^ { 2 } + 2 x - 5$
B) $- 7 x ^ { 3 } + 5 x ^ { 2 } + 15 x - 11$
C) $- 2 x ^ { 3 } + 15 x - 11$
D) $- 2 x ^ { 3 } + 12 x ^ { 2 } - 6 x - 5$

Question 26

Use a vertical format to add the polynomials.
$$\begin{array} { l } 3 x ^ { 7 } + 6 x ^ { 6 } - 5 x \\2 x ^ { 7 } + 3 x ^ { 6 } - 4 x \\\hline\end{array}$$

A) $5 x ^ { 7 } + 9 x ^ { 6 } - 9 x$
B) $5 \times ^ { 14 }$
C) $- 3 x ^ { 7 } + 6 x ^ { 6 } + 2 x$
D) $5 x + 9 x ^ { 7 } - 9 x ^ { 6 }$

Question 27

Subtract the polynomials.
$$\left( 7 x ^ { 2 } + 3 x ^ { 4 } - 6 - 2 x ^ { 3 } \right) - \left( - 8 + 8 x ^ { 3 } + 8 x ^ { 4 } + 3 x ^ { 2 } \right)$$

A) $- 5 x ^ { 4 } + 6 x ^ { 3 } + 10 x ^ { 2 } - 14$
B) $11 x ^ { 4 } + 6 x ^ { 3 } + 10 x ^ { 2 } + 2$
C) $- 5 x ^ { 4 } - 10 x ^ { 3 } + 4 x ^ { 2 } + 2$
D) $11 x ^ { 4 } + 6 x ^ { 3 } + 10 x ^ { 2 } - 14$

Question 28

Use a vertical format to subtract the polynomials.

- $$\begin{array} { r } 12 x ^ { 3 } + 6 x ^ { 2 } \\- \left( 16 x ^ { 3 } - 2 x ^ { 2 } \right) \\\hline\end{array}$$

A) $3 y ^ { 7 } - 18 y ^ { 6 } - 9$
B) $3 y ^ { 7 } - 6 y ^ { 6 } - 15$
C) $3 y ^ { 7 } - 18 y ^ { 6 } - 15$
D) $3 y ^ { 7 } - 6 y ^ { 6 } - 9$

Question 29

Subtract the polynomials.
$\left( 18 y ^ { 4 } - 15 y ^ { 3 } \right) - \left( - 8 y ^ { 4 } - 19 y ^ { 3 } \right)$

A) $26 y ^ { 4 } - 34 y ^ { 3 }$
B) $30 y ^ { 7 }$
C) $10 y ^ { 4 } - 34 y ^ { 3 }$
D) $26 y ^ { 4 } + 4 y ^ { 3 }$

Question 30

Use a vertical format to add the polynomials.
$$\begin{array} { l } - \frac { 1 } { 5 } x ^ { 2 } + \frac { 2 } { 3 } x + \frac { 2 } { 5 } \\- \frac { 3 } { 5 } x ^ { 2 } + \frac { 3 } { 4 } x - \frac { 1 } { 3 } \\\hline\end{array}$$

A) $- \frac { 4 } { 5 } x ^ { 2 } + \frac { 17 } { 12 } x + \frac { 1 } { 15 }$
B) $- \frac { 4 } { 5 } x ^ { 4 } + \frac { 17 } { 12 } x ^ { 2 } + \frac { 1 } { 15 }$
C) $\frac { 6 } { 5 } x ^ { 2 } + 5 x - \frac { 4 } { 3 }$
D) $\frac { 37 } { 60 } x ^ { 6 } + \frac { 1 } { 15 }$

Question 31

Perform the indicated operations.
$$\left[ \left( 3 x ^ { 9 } + 2 \right) - \left( - 12 x ^ { 7 } + 9 x ^ { 3 } \right) \right] - \left[ \left( 7 x ^ { 9 } - 7 x ^ { 5 } + 9 x \right) + \left( 11 x ^ { 3 } - 9 x - 10 \right) \right]$$

A) $4 x ^ { 9 } + 12 x ^ { 7 } + 7 x ^ { 5 } - 20 x ^ { 3 } + 12$
B) $- 4 x ^ { 9 } + 12 x ^ { 7 } - 7 x ^ { 5 } - 20 x ^ { 3 } + 12$
C) $- 4 x ^ { 9 } + 12 x ^ { 7 } + 7 x ^ { 5 } - 20 x ^ { 3 } + 12$
D) $4 x ^ { 9 } + 12 x ^ { 7 } - 7 x ^ { 5 } - 20 x ^ { 3 } + 12$

Question 32

Use a vertical format to add the polynomials.

- $$\begin{array} { r r } 1.5 x ^ { 3 } + 7.7 x ^ { 2 } + & 4.1 \\&- 3.4 x - 2.7 \\- 3.5 x ^ { 2 } + & x + 9.7 \\\hline\end{array}$$

A) $1.5 x ^ { 3 } + 11.2 x ^ { 2 } + 5.4 x - 8.3$
B) $13.1 x ^ { 6 } + 11.1$
C) $1.5 \mathrm { x } ^ { 3 } + 4.2 \mathrm { x } ^ { 2 } + 6.4 \mathrm { x } + 11.1$
D) $1.5 \mathrm { x } ^ { 3 } + 4.2 \mathrm { x } ^ { 2 } + 7.4 \mathrm { x } + 11.1$

Question 33

Subtract the polynomials.
$$\left( 4 x ^ { 6 } - 15 x ^ { 5 } - 19 \right) - \left( 8 x ^ { 5 } + 2 x ^ { 6 } + 2 \right)$$

A) $2 x ^ { 6 } - 23 x ^ { 5 } - 17$
B) $2 x ^ { 6 } - 13 x ^ { 5 } - 17$
C) $- 42 x ^ { 11 }$
D) $2 x ^ { 6 } - 23 x ^ { 5 } - 21$

Question 34

Use a vertical format to subtract the polynomials.

- $$\begin{array} { r } 12 x ^ { 3 } + 6 x ^ { 2 } \\- \left( 16 x ^ { 3 } - 2 x ^ { 2 } \right) \\\hline\end{array}$$

A) $- 4 x ^ { 3 } + 8 x ^ { 2 }$ \end{tabular}
B) $28 x ^ { 3 } + 4 x ^ { 2 }$
C) $- 4 x ^ { 3 } + 4 x ^ { 2 }$
D) $28 x ^ { 3 } + 8 x ^ { 2 }$

Question 35

Use a vertical format to subtract the polynomials.

- $$\begin{array} { r } 9 y ^ { 6 } + 5 y ^ { 4 } + 3 y \\- \left( 2 y ^ { 6 } - 18 y ^ { 4 } + 9 y \right) \\\hline\end{array}$$

A) $7 y ^ { 6 } + 7 y ^ { 4 } - 6 y$
B) $7 y ^ { 6 } + 7 y ^ { 4 } + 12 y$
C) $7 y ^ { 6 } + 23 y ^ { 4 } - 6 y$
D) $7 y ^ { 6 } + 23 y ^ { 4 } + 12 y$

Question 36

Subtract the polynomials.
$\left( 8 x ^ { 6 } - 8 x ^ { 4 } + 12 \right) - \left( 4 x ^ { 6 } + 13 x ^ { 4 } - 8 \right)$

A) $4 x ^ { 6 } - 21 x ^ { 4 } + 20$
B) $4 x ^ { 6 } - 4 x ^ { 4 } + 4$
C) $3 x ^ { 10 }$
D) $4 x ^ { 6 } - 21 x ^ { 4 } + 4$

Question 37

Perform the indicated operations.
The bar graph shows the median annual income for residents of a selected region of the United States, by level of education. The given polynomial models describe the median annual income for men, M, and for women, W, who have
Completed x years of education. $$\begin{array} { l } M = - 23 x ^ { 3 } + 1170 x ^ { 2 } - 13,808 x + 72,566 \\W = 8 x ^ { 3 } - 56 x ^ { 2 } + 511 x + 14,763\end{array}$$ Find a mathematical model for M - W and use it to calculate the difference in the median annual income between
Men and women with 10 years of education. Does the model underestimate or overestimate the actual
Difference?

A) $16,433; overestimates
B) $4987; underestimates
C) $6213; underestimates
D) $9653; overestimates

Question 38

Subtract the polynomials.
$$( 4 x - 7 ) - ( 20 x + 19 )$$

A) $- 16 x + 12$
B) $24 x + 12$
C) $- 42 x ^ { 2 }$
D) $- 16 x - 26$

Question 39

Perform the indicated operations.
Subtract -6 - 2x7 + 5x8 - 9x6 + 9x from the sum of -4x6 + 9x + 9 and 9x8 + 4x7.

A) 4x8 + 6x7 + 5x6 + 15
B) 14x8 + 2x7 - 13x6 + 15
C) 14x8 + 2x7 - 13x6 + 3
D) 4x8 + 2x7 - 13x6 + 3

Question 40

Use a vertical format to subtract the polynomials.
$$\begin{array} { r } 5 x ^ { 6 } + 3 x ^ { 5 } + 2 x ^ { 4 } - 6 \\- \left( 2 x ^ { 6 } - 7 x ^ { 5 } + 4 x ^ { 4 } - 5 \right) \\\hline\end{array}$$

A) $3 x ^ { 6 } - 4 x ^ { 5 } + 6 x ^ { 4 } - 11$
B) $7 x ^ { 6 } - 4 x ^ { 5 } + 6 x ^ { 4 } - 11$
C) $7 x ^ { 6 } - 4 x ^ { 5 } + 6 x ^ { 4 } - 1$
D) $3 x ^ { 6 } + 10 x ^ { 5 } - 2 x ^ { 4 } - 1$

Question 41

Multiply the monomials.
$\left( 6 x ^ { 7 } \right) \left( 4 x ^ { 2 } \right)$

A) $24 x ^ { 14 }$
B) $- 24 x ^ { 14 }$
C) $- 24 x ^ { 9 }$
D) $24 x ^ { 9 }$

Question 42

Graph the equation. Find seven solutions in your table of values for the equation by using integers for x, starting with -3
and ending with 3.

- $$y = 4 - x ^ { 2 }$$
$\begin{array} { r | l } x & 4 - x ^ { 2 } \\\hline - 3 & \\- 2 & \\- 1 & \\0 & \\1 & \\2 & \\3 &\end{array}$

A)
B)
C)
D)

Question 43

Simplify the expression using the products-to-powers rule.
$( - 4 x ) ^ { 3 }$

A) $- 64 x$
B) $- 12 x ^ { 3 }$
C) $- 64 x ^ { 3 }$
D) $- 12 \mathrm { x }$

Question 44

Multiply the expression using the product rule.
$$4 ^ { 8 } \cdot 4 ^ { 6 }$$

A) $16 ^ { 48 }$
B) $4 ^ { 48 }$
C) $16 ^ { 14 }$
D) $4 ^ { 14 }$

Question 45

Multiply the expression using the product rule.
$y ^ { 10 } \cdot y ^ { 2 }$

A) $y ^ { 20 }$
B) $2 y ^ { 20 }$
C) $\mathrm { y } ^ { 12 }$
D) $2 \mathrm { y } ^ { 12 }$

Question 46

Graph the equation. Find seven solutions in your table of values for the equation by using integers for x, starting with -3
and ending with 3.
A census was taken to determine the median annual income for residents of a selected region of the United States, by level of education. The given polynomial models describe the median annual income for men, M, and
For women, W, who have completed x years of education. Shown in a rectangular coordinate system are the
Graphs of the polynomial models. Identify the median annual income for a man with 10 years of education as a
Point on the appropriate graph. $$\begin{array} { l } \mathrm { M } = 224 \mathrm { x } ^ { 2 } - 1266 \mathrm { x } + 20,106 \\\mathrm {~W} = 287 \mathrm { x } ^ { 2 } - 4030 \mathrm { x } + 33,761\end{array}$$

A) (10, 41,240)
B) (10, 58,431)
C) (10, 29,846)
D) (10, 22,161)

Question 47

Multiply the expression using the product rule.
$$x \cdot x ^ { 2 }$$

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

Question 48

Simplify the expression using the products-to-powers rule.
$\left( - 3 x ^ { 2 } \right) ^ { 4 }$

A) $- 3 x ^ { 8 }$
B) $- 81 x ^ { 8 }$
C) $81 x ^ { 6 }$
D) $81 x ^ { 8 }$

Question 49

Simplify the expression using the power rule.
$\left[ \left( - 7 ^ { 5 } \right) \right] ^ { 10 }$

A) $( - 7 ) ^ { 50 }$
B) $( - 49 ) ^ { 50 }$
C) $( - 49 ) ^ { 5 }$
D) $( - 7 ) ^{ 15 }$

Question 50

Perform the indicated operations.
The bar graph shows the median annual income for residents of a selected region of the United States, by level of education. The given polynomial models describe the median annual income for men, M, and for women, W, who have
Completed x years of education. $$\begin{array} { l } M = - 23 x ^ { 3 } + 1170 x ^ { 2 } - 13,808 x + 72,566 \\W = 8 x ^ { 3 } - 56 x ^ { 2 } + 511 x + 14,763\end{array}$$ Find a mathematical model for M - W and use it to calculate the difference in the median annual income between
Men and women with 8 years of education. Does the model underestimate or overestimate the actual
Difference?

A) $4533; underestimates
B) $1325; underestimates
C) $14,019; overestimates
D) $5843; overestimates

Question 51

Multiply the monomials.
$$\left( - 6 x ^ { 5 } \right) \left( 5 x ^ { 3 } \right)$$

A) $- 30 x ^ { 15 }$
B) $30 x ^ { 15 }$
C) $30 x ^ { 8 }$
D) $- 30 x ^ { 8 }$

Question 52

Multiply the expression using the product rule.
$$x ^ { 7 } \cdot x ^ { 7 } \cdot x ^ { 8 }$$

A) $x ^ { 57 }$
B) $x ^ { 15 }$
C) $x ^ { 14 }$
D) $x ^ { 22 }$

Question 53

Simplify the expression using the products-to-powers rule.
$$\left( 2 x ^ { 7 } \right) ^ { 3 }$$

A) $2 x ^ { 21 }$
B) $2 x ^ { 10 }$
C) $8 x ^ { 21 }$
D) $8 \mathrm { x } ^ { 10 }$

Question 54

Graph the equation. Find seven solutions in your table of values for the equation by using integers for x, starting with -3
and ending with 3.

- $$y = x ^ { 2 } - 3$$
$\begin{array} { r | r } x & x ^ { 2 } - 3 \\\hline - 3 & \\- 2 & \\- 1 & \\0 & \\1 & \\2 & \\3 &\end{array}$

A)
B)
C)
D)

Question 55

Graph the equation. Find seven solutions in your table of values for the equation by using integers for x, starting with -3
and ending with 3.
A census was taken to determine the median annual income for residents of a selected region of the United States, by level of education. The given polynomial models describe the median annual income for men, M, and
For women, W, who have completed x years of education. Shown in a rectangular coordinate system are the
Graphs of the polynomial models. Identify the median annual income for a woman with 13 years of education as
A point on the appropriate graph. $$\begin{array} { l } M = 224 x ^ { 2 } - 1266 x + 20,106 \\W = 287 x ^ { 2 } - 4030 x + 33,761\end{array}$$

A) (13, 41,504)
B) (13, 56,696)
C) (13, 29,874)
D) (13, 78,234)

Question 56

Simplify the expression using the power rule.
$\left( y ^ { 2 } \right) ^ { 8 }$

A) $\mathrm { y } ^ { 10 }$
B) $8 \mathrm { y } ^ { 16 }$
C) $\mathrm { y } ^ { 16 }$
D) $8 \mathrm { y } ^ { 2 }$

Question 57

Graph the equation. Find seven solutions in your table of values for the equation by using integers for x, starting with -3
and ending with 3.

- $$y = x ^ { 2 } + 4$$
$\begin{array} { r | r } x & x ^ { 2 } + 4 \\\hline - 3 & \\- 2 & \\- 1 & \\0 & \\1 & \\2 & \\3 &\end{array}$

A)
B)
C)
D)

Question 58

Simplify the expression using the products-to-powers rule.
$$\left( - 3 x ^ { 6 } \right) ^ { 3 }$$

A) $- 3 x ^ { 18 }$
B) $- 27 x ^ { 18 }$
C) $27 x ^ { 18 }$
D) $- 27 x ^ { 9 }$

Question 59

Simplify the expression using the products-to-powers rule.
$( 3 x ) ^ { 2 }$

A) $9 x ^ { 2 }$
B) $9 x$
C) $6 x$
D) $6 x ^ { 2 }$

Question 60

Simplify the expression using the power rule.
$\left( 5 ^ { 6 } \right) ^ { 5 }$

A) $5 ^ { 30 }$
B) $25 ^ { 6 }$
C) $25 ^ { 30 }$
D) $5 ^ { 11 }$

Question 61

Find the product.
$( 9 x - 1 ) \left( x ^ { 2 } - 5 x + 1 \right)$

A) $9 x ^ { 3 } - 44 x ^ { 2 } + 4 x - 1$
B) $9 x ^ { 3 } + 46 x ^ { 2 } - 14 x + 1$
C) $9 x ^ { 3 } - 46 x ^ { 2 } + 14 x - 1$
D) $9 x ^ { 3 } - 45 x ^ { 2 } + 9 x + 1$

Question 62

Find the product.
$$( x + 9 ) ( x + 11 )$$

A) $x ^ { 2 } + 99 x + 20$
B) $x ^ { 2 } + 20 x + 19$
C) $x ^ { 2 } + 20 x + 99$
D) $x ^ { 2 } + 19 x + 99$

Question 63

Find the product.
$$( 2 x - 10 ) ( x + 9 )$$

A) $x ^ { 2 } - 90 x + 8$
B) $2 x ^ { 2 } + 7 x - 90$
C) $x ^ { 2 } + 8 x + 7$
D) $2 x ^ { 2 } + 8 x - 90$

Question 64

Solve the problem.
Find the area of a triangle with a base of 7x inches and a height of (10x + 4) inches.

A) $\left( 17 x ^ { 2 } + 11 x \right)$ sq. in.
B) $\left( 35 x ^ { 2 } + 14 x \right)$ sq. in.
C) $\left( 70 x ^ { 2 } + 28 x \right)$ sq. in.
D) $( 35 x + 14 )$ sq. in.

Question 65

Multiply the monomials.
$$\left( \frac { 1 } { 4 } x ^ { 8 } \right) \left( \frac { 1 } { 5 } x ^ { 2 } \right)$$

A) $- \frac { 1 } { 20 } x ^ { 16 }$
B) $- \frac { 1 } { 20 } x ^ { 10 }$
C) $\frac { 1 } { 20 } x ^ { 10 }$
D) $\frac { 1 } { 20 } x ^ { 16 }$

Question 66

Find the product.
$11 x ^ { 7 } \left( 5 x ^ { 7 } - 10 x ^ { 5 } - 11 \right)$

A) $55 x ^ { 14 } - 110 x ^ { 12 } - 121 x ^ { 7 }$
B) $55 \mathrm { x } ^ { 14 } - 110 \mathrm { x } ^ { 12 }$
C) $55 x ^ { 7 } - 110 x ^ { 5 } - 121$
D) $55 x ^ { 14 } - 10 x ^ { 5 } - 11$

Question 67

Find the product.
$$6 x ^ { 5 } ( 2 x + 8 )$$

A) $12 x ^ { 6 } + 48 x ^ { 5 }$
B) $12 x + 48$
C) $60 x ^ { 5 }$
D) $12 x ^ { 6 } + 8$

Question 68

Multiply the monomials.
$\left( - \frac { 1 } { 5 } x ^ { 7 } \right) \left( \frac { 1 } { 4 } x ^ { 9 } \right)$

A) $\frac { 1 } { 20 } x ^ { 16 }$
B) $- \frac { 1 } { 20 } x ^ { 16 }$
C) - \frac { 1 } { 20 } x ^ { 63 }\)
D) $\frac { 1 } { 20 } x ^ { 63 }$

Question 69

Multiply the monomials.
$$\left( 4 x ^ { 5 } \right) \left( - 9 x ^ { 4 } \right)$$

A) $36 x ^ { 9 }$
B) $- 36 x ^ { 9 }$
C) $36 x ^ { 20}$
D) $- 36 x ^ { 20 }$

Question 70

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

A) $- 24 x ^ { 18 }$
B) $24 \mathrm { x } ^ { 11 }$
C) $- 24 x ^ { 11}$
D) $24 \mathrm { x } ^ { 18 }$

Question 71

Find the product.
$$- 6 x ^ { 4 } \left( 8 x ^ { 5 } + 7 \right)$$

A) $- 48 x ^ { 5 } - 42$
B) $- 48 x ^ { 9 } - 42 x ^ { 4 }$
C) $- 48 x ^ { 9 } + 7$
D) $- 90 x ^ { 4 }$

Question 72

Multiply the monomials.
$$\left( - \frac { 1 } { 8 } x ^ { 9 } \right) \left( - \frac { 1 } { 9 } x ^ { 8 } \right)$$

A) $\frac { 1 } { 72 } x ^ { 72 }$
B) $\frac { 1 } { 72 } x ^ { 17 }$
C) $=- \frac { 1 } { 72 } x ^ { 72 }$
D) $=- \frac { 1 } { 72 } x ^ { 17 }$

Question 73

Find the product.
$$\left( x ^ { 2 } - 3 x + 1 \right) ( 5 x )$$

A) $5 x ^ { 3 } - 15 x ^ { 2 } + 5 x$
B) $5 x ^ { 3 } - 14 x ^ { 2 } + 2 x$
C) $5 x ^ { 3 } - 15 x ^ { 2 } - 8 x$
D) $5 x ^ { 3 } + 16 x ^ { 2 } + 5 x$

Question 74

Find the product.
$- 7 x ( x - 8 )$

A) $- 7 x ^ { 2 } + 56 x$
B) $x ^ { 2 } + 56 x$
C) $- 7 x ^ { 2 } - 8 x$
D) $49 \mathrm { x } ^ { 2 }$

Question 75

Find the product.
$( x - 5 ) \left( x ^ { 2 } + 5 x - 9 \right)$

A) $x ^ { 3 } + 16 x - 45$
B) $x ^ { 3 } - 34 x + 45$
C) $x ^ { 3 } + 10 x ^ { 2 } + 34 x - 45$
D) $x ^ { 3 } - 10 x ^ { 2 } - 34 x + 45$

Question 76

Find the product.
$$x ( x - 5 )$$

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

Question 77

Multiply the monomials.
$\left( \frac { 1 } { 8 } x ^ { 3 } \right) \left( - \frac { 1 } { 3 } x ^ { 8 } \right)$

A) $= \frac { 1 } { 24 } x ^ { 24 }$
B) $= \frac { 1 } { 24 } x ^ { 11 }$
C) $\frac { 1 } { 24 } x ^ { 24 }$
D) $\frac { 1 } { 24 } x ^ { 11 }$

Question 78

Find the product.
$$5 x ^ { 6 } \left( 12 x ^ { 7 } + 8 x ^ { 5 } \right)$$

A) $100 x ^ { 6 }$
B) $60 x ^ { 13 } + 8 x ^ { 5 }$
C) $60 x ^ { 13 } + 40 x ^ { 11 }$
D) $100 x ^ { 13 } + 100 x ^ { 11 }$

Question 79

Find the product.
$$\left( \frac { 1 } { 4 } x - 9 \right) \left( \frac { 1 } { 3 } x + 8 \right)$$

A) $\frac { 1 } { 12 } x ^ { 2 } - 12 x - 12$
B) $\frac { 1 } { 12 } x ^ { 2 } - 36 x - 72$
C) $- \frac { 1 } { 12 } x ^ { 2 } - 1 x - 72$
D) $\frac { 1 } { 12 } x ^ { 2 } - 1 x - 72$

Question 80

Solve the problem.
Write an expression for the area of the larger rectangle below in two different ways.

A) $y ( 3 y + 8 ) ; 3 y ^ { 2 } + 8 y$
B) $8 ( 3 y + y )$ ; $32 y$
C) $3 y ( y + 8 )$ ; $3 y ^ { 2 } + 24 y$
D) $2 y ( 6 y + 16 ) ; 12 y ^ { 2 } + 32 y$