Deck 5: Polynomials, Polynomial Functions, and Factoring

Question 1

Use the graph to estimate the average number of minutes a woman exercised per week if her average monthly weight loss was 4.4 pounds. A) 115 min B) 120 min C) 135 min D) 127 min Answer: B Determine whether the graph shown is the graph of a polynomial function.

A) Yes
B) No

Answer 1

A

Question 2

Find the indicated function value.
Find $f ( 2 )$ when $f ( x ) = x ^ { 3 } + 4 x ^ { 2 } + 9 x$ .

A) $- 6$
B) 26
C) 6
D) 42

Answer 2

D

Question 3

Give the requested components for the polynomial.
$5 x ^ { 8 } y + x ^ { 7 } y ^ { 3 } + 13 y ^ { 2 }$ ; leading term and leading coefficient of the polynomial

A) leading term: $5 x ^ { 8 } y$ ; leading coefficient: 5
B) leading term: $x ^ { 7 } y ^ { 3 }$ ; leading coefficient: 1
C) leading term: $13 y ^ { 2 }$ ; leading coefficient: 13
D) leading term: $\mathrm { x } ^ { 7 } \mathrm { y } ^ { 3 }$ ; leading coefficient: 13

Answer 3

B

Question 4

Find the indicated function value.
Find $f ( 0 )$ when $f ( x ) = x ^ { 2 } - 3 x - 1$

A) 0
B) $- 1$
C) 1
D) 1

Question 5

Solve the problem.
A rocket is stopped 28 feet from a satellite when it begins accelerating away from the satellite at a constant rate of 10 feet per second per second. The distance between the rocket and the satellite is given by the polynomial $\mathrm { P } ( \mathrm { t } ) = 5 \mathrm { t } ^ { 2 } + 28$ . Find the distance between the rocket and the satellite 9 seconds after the rocket started moving.

A) $109 \mathrm { ft }$
B) $73 \mathrm { ft }$
C) $405 \mathrm { ft }$
D) $433 \mathrm { ft }$

Question 6

Use the graph to estimate the average number of minutes a woman exercised per week if her average monthly weight loss was 4.4 pounds. A) 115 min B) 120 min C) 135 min D) 127 min Answer: B Determine whether the graph shown is the graph of a polynomial function.

A) Yes
B) No

Question 7

Solve the problem.
The following table shows the number of speeding tickets issued in a certain state for the past five years. $$\begin{array} { c | c } \text { Year } & \text { Speeding Tickets Issued } \\\hline 1 & 2500 \\2 & 2544 \\3 & 2601 \\4 & 2637 \\5 & 2690\end{array}$$ The polynomial function f(x) = -0.63x3 + 0.55x² + 61.16x + 2439.2 models the number of speeding tickets issued over the past five years. Use this function to predict the number of speeding tickets issued in year 15. Round to the nearest whole number.

A) 437 speeding tickets issued
B) 1354 speeding tickets issued
C) -1075 speeding tickets issued
D) 1339 speeding tickets issued

Question 8

Use the graph to estimate the average number of minutes a woman exercised per week if her average monthly weight loss was 4.4 pounds. A) 115 min B) 120 min C) 135 min D) 127 min Answer: B Determine whether the graph shown is the graph of a polynomial function.

A) Yes
B) No

Question 9

Find the indicated function value.
Find $f ( 4 )$ when $f ( x ) = x ^ { 2 } - 5 x - 7$

A) 3
B) 43
C) $- 11$
D) 29

Question 10

Use the graph to estimate the average number of minutes a woman exercised per week if her average monthly weight loss was 4.4 pounds. A) 115 min B) 120 min C) 135 min D) 127 min Answer: B Determine whether the graph shown is the graph of a polynomial function.

A) Yes
B) No

Question 11

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph.
$$f ( x ) = - 3 x ^ { 2 } - 2 x + 2$$

A) rises to the left and rises to the right

B) rises to the left and falls to the right

C) falls to the left and falls to the right

D) falls to the left and rises to the right

Question 12

Find the indicated function value.
Find $f ( - 1 )$ when $f ( x ) = 5 x ^ { 2 } - 3 x + 6$

A) 10
B) 14
C) 8
D) 2

Question 13

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph.
$$f ( x ) = 6 x ^ { 3 } - 3 x ^ { 2 } - 3 x - 2$$

A) rises to the left and rises to the right

B) falls to the left and falls to the right

C) rises to the left and falls to the right

D) falls to the left and rises to the right

Question 14

Give the requested components for the polynomial.
$7 x ^ { 8 } - 12 x ^ { 5 } y ^ { 5 } - x y ^ { 2 } + 3$ ; the leading term and the coefficient of each term

A) leading term: 10; coefficients: $8,10,3$ , and 0
B) leading term: $7 x ^ { 8 }$ ; coefficients: $7,12,1$ , and 3
C) leading term: 8 ; coefficients: 8,5 , and 1
D) leading term: $- 12 x ^ { 5 } y ^ { 5 }$ ; coefficients: $7 , - 12 , - 1$ , and 3

Question 15

Give the requested components for the polynomial.
$- 5 x ^ { 3 } + 6 x ^ { 2 } + 4 x$ ; the degree of the polynomial and the leading coefficient of the polynomial.

A) degrees: 3,2 , and 1 ; coefficients: $- 5,6$ , and 4
B) degree: $- 5$ ; coefficient: 3
C) degree: 3 ; coefficient: $- 5$
D) degrees: $- 5,6$ , and 4 ; coefficients: 3,2 , and 0

Question 16

Use the graph to estimate the average number of minutes a woman exercised per week if her average monthly weight loss was 4.4 pounds. A) 115 min B) 120 min C) 135 min D) 127 min Answer: B Determine whether the graph shown is the graph of a polynomial function.

A) Yes
B) No

Question 17

Use the graph to estimate the average number of minutes a woman exercised per week if her average monthly weight loss was 4.4 pounds. A) 115 min B) 120 min C) 135 min D) 127 min Answer: B Determine whether the graph shown is the graph of a polynomial function.

A) Yes
B) No

Question 18

Give the requested components for the polynomial.
$x ^ { 5 } - 2 x ^ { 4 } y ^ { 8 } + 11 x y - 7 x + 9$ ; degree of each term and degree of the polynomial

A) degrees: $5,12,2,1$ , 0; degree of polynomial: 12
B) degrees: $5,4,2,0$ ; degree of polynomial: 19
C) degrees: $1 , - 2,11 , - 7,9$ ; degree of polynomial: $- 2$
D) degrees: $5,4,1,1,0$ ; degree of polynomial: 5

Question 19

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph.
$$f ( x ) = 2 x ^ { 2 } - 3 x - 2$$

A) rises to the left and falls to the right

B) falls to the left and falls to the right

C) falls to the left and rises to the right

D) rises to the left and rises to the right

Question 20

Give the requested components for the polynomial.
$\mathrm { x } ^ { 5 } - 10 \mathrm { x } ^ { 2 }$ ; the degree of each term and the coefficient of each term

A) degrees: 1 and 5; coefficients: $- 10$ and 2
B) degrees: 5 and 2; coefficients: 1 and $- 10$
C) degrees: 1 and $- 10$ ; coefficients: 5 and 2
D) degrees: 5 and 2; coefficients: 0 and 10

Question 21

Add the polynomials. Assume all variable exponents represent whole numbers.
$$\left( \frac { 3 } { 5 } x ^ { 2 } + \frac { 3 } { 4 } x - \frac { 4 } { 5 } \right) + \left( \frac { 3 } { 4 } x ^ { 2 } - \frac { 2 } { 5 } x - \frac { 1 } { 4 } \right)$$

A) $\frac { 27 } { 20 } x ^ { 2 } + \frac { 7 } { 20 } x - \frac { 21 } { 20 }$
B) $\frac { 27 } { 20 } x ^ { 4 } + \frac { 7 } { 20 } x ^ { 2 } - \frac { 21 } { 20 }$
C) $\frac { 9 } { 2 } x ^ { 2 } - 3 x + 2$
D) $\frac { 17 } { 10 } x ^ { 6 } - \frac { 21 } { 20 }$

Question 22

Add the polynomials. Assume all variable exponents represent whole numbers.
$$\left( - 9 x ^ { 7 } + 18 x ^ { 6 } - 13 \right) + \left( 3 x ^ { 7 } + 16 x ^ { 6 } - 9 \right)$$

A) $- 6 x ^ { 7 } + 34 x ^ { 6 } - 22$
B) $6 \times 13$
C) $- 6 x ^ { 7 } + 25 x ^ { 6 } + 4$
D) $- 6 x ^ { 7 } + 34 x ^ { 6 } + 4$

Question 23

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph.
$$f ( x ) = 4 x ^ { 4 } - 3 x ^ { 2 }$$

A) rises to the left and rises to the right

B) falls to the left and falls to the right

C) rises to the left and falls to the right

D) falls to the left and rises to the right

Question 24

Subtract the polynomials. Assume all variable exponents represent whole numbers.
$\left( 9 x ^ { 6 } - 6 x ^ { 5 } + 15 x \right) - \left( 2 x ^ { 6 } + 12 x ^ { 5 } + 19 x \right)$

A) $7 x ^ { 6 } - 4 x ^ { 5 } + 34 x$
B) $7 x ^ { 6 } - 18 x ^ { 5 } - 4 x$
C) $- 15 x ^ { 12 }$
D) $7 x ^ { 6 } - 18 x ^ { 5 } + 34 x$

Question 25

Subtract the polynomials. Assume all variable exponents represent whole numbers.
$\left( 10 x ^ { 8 } + 4 x ^ { 7 } - 11 x ^ { 2 } + 9 \right) - \left( 6 x ^ { 8 } - 6 x ^ { 5 } + 5 x ^ { 2 } - 3 \right)$

A) $4 x ^ { 8 } + 4 x ^ { 7 } + 6 x ^ { 5 } - 16 x ^ { 2 } + 12$
B) $- 4 x ^ { 8 } + 4 x ^ { 7 } - 6 x ^ { 5 } - 16 x ^ { 2 } + 12$
C) $4 x ^ { 8 } + 4 x ^ { 7 } - 6 x ^ { 5 } - 16 x ^ { 2 } + 12$
D) $- 4 x ^ { 8 } + 4 x ^ { 7 } + 6 x ^ { 5 } - 16 x ^ { 2 } + 12$

Question 26

Solve the problem.
A herd of bison is introduced to a wildlife refuge. The number of bison, $\mathrm { N } ( \mathrm { t } )$ , after $t$ years is described by the polynomial function $N ( t ) = - t ^ { 4 } + 23 t + 120$ . Use the Leading Coefficient Test to determine the graph's end behavior. What does this mean about what will eventually happen to the bison population?

A) The bison population in the refuge will be displaced by "oil" wells.
B) The bison population in the refuge will grow out of control.
C) The bison population in the refuge will reach a constant amount greater than 0 .
D) The bison population in the refuge will die out.

Question 27

Subtract the polynomials. Assume all variable exponents represent whole numbers.
$$\left( x ^ { 3 } + 7 x y - 4 y ^ { 2 } \right) - \left( 8 x ^ { 3 } + 4 x y + y ^ { 2 } \right)$$

A) $9 x ^ { 3 } + 3 x y - 5 y ^ { 2 }$
B) $7 x ^ { 3 } - 3 x y - 3 y ^ { 2 }$
C) $- 7 x ^ { 3 } + 3 x y - 3 y ^ { 2 }$
D) $- 7 x ^ { 3 } + 3 x y - 5 y ^ { 2 }$

Question 28

Add the polynomials. Assume all variable exponents represent whole numbers.
$$\left( - 8 x ^ { 7 } - 5 x ^ { 6 } + 2 x ^ { 5 } + 2 \right) + \left( 5 x ^ { 7 } - 8 x ^ { 6 } + 6 x ^ { 5 } + 5 \right)$$

A) $- 3 x ^ { 7 } - 3 x ^ { 6 } + 4 x ^ { 5 } + 3$
В) $13 x ^ { 7 } - 3 x ^ { 6 } + 4 x ^ { 5 } + 3$
C) $13 x ^ { 7 } - 3 x ^ { 6 } + 4 x ^ { 5 } + 7$
D) $- 3 x ^ { 7 } - 13 x ^ { 6 } + 8 x ^ { 5 } + 7$

Question 29

Subtract the polynomials. Assume all variable exponents represent whole numbers.
$$\left( 7 x ^ { 6 } - 10 x ^ { 3 } - 2 \right) - \left( 3 x ^ { 6 } - 20 x ^ { 3 } - 17 \right)$$

A) $4 x ^ { 6 } + 10 x ^ { 3 } + 15$
B) $29 \mathrm { x } ^ { 9 }$
C) $4 x ^ { 6 } - 7 x ^ { 3 } - 19$
D) $4 x ^ { 6 } + 10 x ^ { 3 } - 19$

Question 30

Add the polynomials. Assume all variable exponents represent whole numbers.
$$\left( 5 x ^ { 2 n } - x ^ { n } - 1 \right) + \left( x ^ { 2 n } + 4 x ^ { n } + 10 \right)$$

A) $4 x ^ { 4 n } - 5 x ^ { 2 n } - 11$
B) $6 x ^ { 2 n } + 3 x ^ { n } + 9$
C) $5 x ^ { 2 n } + 4 x ^ { n } + 10$
D) $6 x ^ { 4 n } + 5 x ^ { 2 n } + 11$

Question 31

Add the polynomials. Assume all variable exponents represent whole numbers.
$$\left( 12 x ^ { 2 } y - 10 x y + 11 \right) + \left( - 11 x ^ { 2 } y + 4 x y - 6 \right)$$

A) $x ^ { 2 } y - 6 x y + 5$
B) $23 x ^ { 2 } y + 14 x y + 17$
C) $- x ^ { 2 } y - 14 x y + 17$
D) $- 6 x ^ { 3 } y ^ { 2 } + 5$

Question 32

Subtract the polynomials. Assume all variable exponents represent whole numbers.
$$\left( 4 x ^ { 5 } + 5 x ^ { 4 } - 6 x ^ { 3 } - 9 \right) - \left( 6 x ^ { 5 } + 9 x ^ { 4 } + 9 x ^ { 3 } - 6 \right)$$

A) $10 x ^ { 5 } + 14 x ^ { 4 } + 3 x ^ { 3 } - 15$
B) $- 2 x ^ { 5 } - 4 x ^ { 4 } - 15 x ^ { 3 } - 3$
C) $10 x ^ { 5 } + 14 x ^ { 4 } + 3 x ^ { 3 } - 3$
D) $- 2 x ^ { 5 } + 14 x ^ { 4 } + 3 x ^ { 3 } - 15$

Question 33

Add the polynomials. Assume all variable exponents represent whole numbers.
$$\left( 3 y ^ { 2 n } + 5 y ^ { n } + 4 \right) + \left( 5 y ^ { 2 n } + 5 y ^ { n } + 8 \right)$$

A) $8 y ^ { 4 n } + 10 y ^ { 2 n } + 12$
B) $9 y ^ { 2 n } + 8 y ^ { n } + 13$
C) $30 y ^ { 3 n }$
D) $8 y ^ { 2 n } + 10 y ^ { n } + 12$

Question 34

Subtract the polynomials. Assume all variable exponents represent whole numbers.
$$\left( 3 x ^ { 6 } - 15 x ^ { 3 } - 11 \right) - \left( 9 x ^ { 6 } - 20 x ^ { 3 } + 3 \right)$$

A) $- 6 x ^ { 6 } + 5 x ^ { 3 } - 14$
B) $- 15 x ^ { 9 }$
C) $- 6 x ^ { 6 } + 5 x ^ { 3 } - 8$
D) $- 6 x ^ { 6 } - 6 x ^ { 3 } - 8$

Question 35

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph.
$$f ( x ) = - 6 x ^ { 3 } + 3 x ^ { 2 } + 3 x + 2$$

A) falls to the left and falls to the right

B) rises to the left and falls to the right

C) rises to the left and rises to the right

D) falls to the left and rises to the right

Question 36

Add the polynomials. Assume all variable exponents represent whole numbers.
$$\left( \frac { 1 } { 8 } x ^ { 4 } + \frac { 2 } { 5 } x ^ { 3 } - \frac { 1 } { 6 } x + 7 \right) + \left( - \frac { 5 } { 8 } x ^ { 4 } - \frac { 1 } { 5 } x ^ { 3 } + \frac { 1 } { 3 } x - 9 \right)$$

A) $\frac { 3 } { 4 } x ^ { 8 } + \frac { 3 } { 5 } x ^ { 6 } + \frac { 1 } { 2 } x ^ { 2 } + 16$
B) $\frac { 3 } { 4 } x ^ { 4 } + \frac { 3 } { 5 } x ^ { 3 } + \frac { 1 } { 2 } x + 16$
C) $\frac { 1 } { 8 } x ^ { 8 } + \frac { 2 } { 5 } x ^ { 6 } - \frac { 1 } { 6 } x ^ { 2 } + 7$
D) $- \frac { 1 } { 2 } x ^ { 4 } + \frac { 1 } { 5 } x ^ { 3 } + \frac { 1 } { 6 } x - 2$

Question 37

Add the polynomials. Assume all variable exponents represent whole numbers.
$$\left( 2 x ^ { 9 } - 6 x ^ { 8 } - 7 x ^ { 7 } - 8 \right) + \left( 4 x ^ { 9 } + 8 x ^ { 8 } + 3 x ^ { 7 } + 4 \right)$$

A) $6 x ^ { 18 } + 2 x ^ { 16 } - 4 x ^ { 14 } - 4$
B) $0 x ^ { 9 } + 0 x ^ { 8 } + 6 x ^ { 7 } - 2$
C) $6 x ^ { 9 } + 2 x ^ { 8 } - 4 x ^ { 7 } - 4$
D) $4 x ^ { 48 } - 4$

Question 38

Add the polynomials. Assume all variable exponents represent whole numbers.
$$\left( 12 x ^ { 5 } y ^ { 3 } + 10 x ^ { 3 } y ^ { 2 } + 2 x y \right) + \left( 4 x ^ { 5 } y ^ { 3 } + 5 x ^ { 3 } y + 3 x y \right)$$

A) $16 x ^ { 5 } y ^ { 3 } + 15 x ^ { 3 } y ^ { 2 } + 5 x y$
B) $16 x ^ { 5 } y ^ { 3 } + 15 x ^ { 3 } y + 5 x y$
C) $15 x ^ { 6 } y ^ { 3 } + 16 x ^ { 5 } y ^ { 3 } + 5 x y$
D) $16 x ^ { 5 } y ^ { 3 } + 10 x ^ { 3 } y ^ { 2 } + 5 x ^ { 3 } y + 5 x y$

Question 39

Add the polynomials. Assume all variable exponents represent whole numbers.
$$\left( - 4 x ^ { 2 } y - x y \right) + \left( 8 x ^ { 2 } y + 7 x y \right)$$

A) $4 x ^ { 2 } y + 6 x y$
B) $12 x ^ { 2 } y + 8 x y$
C) $12 x ^ { 2 } y + 6 x y$
D) $4 x ^ { 2 } y + 8 x y$

Question 40

Add the polynomials. Assume all variable exponents represent whole numbers.
$$\left( 4 x ^ { 6 } - 8 x ^ { 4 } + 8 x \right) + \left( 5 x ^ { 6 } - 2 x ^ { 4 } + 5 x \right)$$

A) $9 x - 10 x ^ { 6 } + 13 x ^ { 4 }$
B) $13 x ^ { 6 } + 2 x ^ { 4 } - 3 x$
C) $12 x ^ { 11 }$
D) $9 x ^ { 6 } - 10 x ^ { 4 } + 13 x$

Question 41

Multiply the monomial and the polynomial. Assume any variable exponents represent whole numbers.
$5 x y ( 3 x - 9 y )$

A) $15 x ^ { 2 } y - 45 x y ^ { 2 }$
B) $8 x ^ { 2 } y - 14 x y ^ { 2 }$
C) $8 x ^ { 2 } - 14 y ^ { 2 }$
D) $15 x ^ { 2 } - 45 y ^ { 2 }$

Question 42

Find the product. Assume all variable exponents represent whole numbers.
$$( x + 3 ) \left( 6 x ^ { 2 } + 2 x + 5 \right)$$

A) $24 x ^ { 3 } + 8 x ^ { 2 } + 20 x$
B) $36 x ^ { 4 } + 6 x ^ { 3 } + 30 x ^ { 2 } + 15$
C) $6 x ^ { 3 } + 18 x ^ { 2 } + 6 x + 15$
D) $6 x ^ { 3 } + 20 x ^ { 2 } + 11 x + 15$

Question 43

Find the product. Assume all variable exponents represent whole numbers.
$$( x - 11 ) \left( x ^ { 2 } + 2 x - 8 \right)$$

A) $x ^ { 3 } - 9 x ^ { 2 } - 30 x + 88$
B) $x ^ { 3 } + 13 x ^ { 2 } + 30 x + 88$
C) $x ^ { 3 } + 13 x ^ { 2 } + 14 x - 88$
D) $x ^ { 3 } - 9 x ^ { 2 } - 14 x - 88$

Question 44

Multiply the monomial and the polynomial. Assume any variable exponents represent whole numbers.
$- 5 x ^ { 5 } ( 11 x + 2 )$

A) $- 55 x ^ { 6 } + 2$
B) $- 55 x - 10$
C) $- 65 x ^ { 5 }$
D) $- 55 x ^ { 6 } - 10 x ^ { 5 }$

Question 45

Find the product. Assume all variable exponents represent whole numbers.
$$( x + 6 ) \left( x ^ { 2 } + 3 x - 2 \right)$$

A) $x ^ { 4 } + 6 x ^ { 3 } + 3 x ^ { 2 } + 16 x - 12$
В) $x ^ { 3 } + 9 x ^ { 2 } + 16 x - 12$
C) $x ^ { 3 } + 9 x ^ { 2 } + 20 x - 12$
D) $x ^ { 3 } + 9 x ^ { 2 } + 20 x + 12$

Question 46

Multiply the monomials. Assume any variable exponents represent whole numbers.
$$\left( 12 x ^ { 5 } y ^ { 7 } z \right) \left( - 9 x ^ { 2 } y z ^ { 3 } \right)$$

A) $3 x ^ { 10 } y ^ { 7 } z ^ { 3 }$
B) $- 108 x ^ { 10 } y ^ { 7 } z ^ { 3 }$
C) $- 108 x ^ { 7 } y ^ { 8 } z ^ { 4 }$
D) $3 x ^ { 7 } y ^ { 8 } z ^ { 4 }$

Question 47

Multiply the monomials. Assume any variable exponents represent whole numbers.
$$\left( 6 x ^ { 4 } \right) \left( 7 x ^ { 7 } \right)$$

A) $- 42^{ 11}$
B) $42 x^{ 11}$
C) $42 x ^ { 28 }$
D) $- 42 \mathrm { x } ^ { 28 }$

Question 48

Multiply the monomials. Assume any variable exponents represent whole numbers.
$$\left( 3 x ^ { 4 } y \right) \left( - 6 x ^ { 7 } y ^ { 2 } \right)$$

A) $- 3 x ^ { 28 } y ^ { 2 }$
B) $- 18 x ^ { 11 } y ^ { 3 }$
C) $- 18 x ^ { 11 } y ^ { 2 }$
D) $- 3 x ^ { 11 } y ^ { 3 }$

Question 49

Multiply the monomial and the polynomial. Assume any variable exponents represent whole numbers.
$12 a b ^ { 2 } \left( 9 a ^ { 2 } b ^ { 3 } + 10 a b \right)$

A) $108 a ^ { 3 } b ^ { 5 } + 120 a ^ { 2 } b ^ { 3 }$
B) $108 a ^ { 3 } b ^ { 4 } + 120 a ^ { 2 } b ^ { 3 }$
C) $108 a ^ { 2 } b ^ { 5 } + 120 a ^ { 2 } b ^ { 3 }$
D) $108 a ^ { 3 } b ^ { 5 } + 120 a ^ { 2 } b ^ { 2 }$

Question 50

Multiply the monomial and the polynomial. Assume any variable exponents represent whole numbers.
$$5 x ^ { 5 } \left( - 4 x ^ { 4 } + 7 x ^ { 2 } - 9 \right)$$

A) $- 20 x ^ { 9 } + 35 x ^ { 7 }$
B) $- 20 x ^ { 4 } + 35 x ^ { 2 } - 45$
C) $- 20 x ^ { 9 } + 7 x ^ { 2 } - 9$
D) $- 20 x ^ { 9 } + 35 x ^ { 7 } - 45 x ^ { 5 }$

Question 51

Multiply the monomial and the polynomial. Assume any variable exponents represent whole numbers.
$6 y \left( 5 y ^ { 2 } - 11 y \right)$

A) $30 y ^ { 2 } - 66 y ^ { 2 }$
B) $30 y ^ { 3 } + 66 y ^ { 2 }$
C) $30 y ^ { 3 } - 66 y ^ { 2 }$
D) $30 y ^ { 3 } - 66 y$

Question 52

Subtract the polynomials. Assume all variable exponents represent whole numbers.
$$\left( 4 x ^ { 4 } + 5 x y - y ^ { 3 } \right) - \left( x ^ { 4 } + 3 x y + 5 y ^ { 3 } \right)$$

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

Question 53

Subtract the polynomials. Assume all variable exponents represent whole numbers.
$$\left( 5 x ^ { 4 } y ^ { 2 } + 7 x ^ { 3 } y + 6 y \right) - \left( 3 x ^ { 4 } y ^ { 2 } + 10 x ^ { 3 } y + 11 y + 9 x \right)$$

A) $2 x ^ { 4 } y ^ { 2 } - 3 x ^ { 3 } y - 5 y + 9 x$
B) $8 x ^ { 4 } y ^ { 2 } + 17 x ^ { 3 } y + 17 y + 9 x$
C) $2 x ^ { 4 } y ^ { 2 } + 3 x ^ { 3 } y - 5 y - 9 x$
D) $2 x ^ { 4 } y ^ { 2 } - 3 x ^ { 3 } y - 5 y - 9 x$

Question 54

Multiply the monomial and the polynomial. Assume any variable exponents represent whole numbers.
$4 x ^ { n } \left( 2 x ^ { 3 n } + 3 x ^ { n } + \frac { 1 } { 4 } x \right)$

A) $8 x ^ { 4 n } + 12 x ^ { 2 n } + 1 x ^ { n } + 1$
B) $8 x ^ { 4 n } + 12 x ^ { n } + 1 x ^ { n } + 1$
C) $8 x ^ { 4 n } - 12 x ^ { 2 n } - 1 x ^ { n } + 1$
D) $8 x ^ { 4 n } + 12 x ^ { 2 n } + 1 x ^ { n }$

Question 55

Subtract the polynomials. Assume all variable exponents represent whole numbers.
$$\left( 4 y ^ { 2 n } + 4 y ^ { n } - 1 \right) - \left( 5 y ^ { 2 n } + 6 y ^ { n } + 4 \right)$$

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

Question 56

Multiply the monomials. Assume any variable exponents represent whole numbers.
$\left( - 6 x ^ { 3 n } y ^ { n } + 2 \right) \left( \frac { 1 } { 12 } x ^ { n } y ^ { 7 } \right)$

A) $- \frac { 1 } { 2 } x ^ { 3 n ^ { 2 } } y ^ { 7 n } + 14$
B) $- \frac { 1 } { 2 } x ^ { 4 n } y ^ { 2 n + 9 }$
C) $- \frac { 1 } { 2 } x ^ { 3 n } y ^ { n } + 9$
D) $- \frac { 1 } { 2 } x ^ { 4 } y ^ { n } + 9$

Question 57

Subtract the polynomials. Assume all variable exponents represent whole numbers.
Subtract $9 x ^ { 3 } + 11 x ^ { 2 } y + 8 x y ^ { 2 } + 10 y ^ { 3 }$ from $2 x ^ { 3 } + 3 x y ^ { 2 } + 12 y ^ { 3 }$

A) $7 x ^ { 3 } + 11 x ^ { 2 } y + 5 x y ^ { 2 } - 2 y ^ { 3 }$
B) $- 7 x ^ { 3 } - 11 x ^ { 2 } y - 5 x y ^ { 2 } + 2 y ^ { 3 }$
C) $11 x ^ { 3 } + 11 x ^ { 2 } y + 10 x y ^ { 2 } + 22 y ^ { 3 }$
D) $- 7 x ^ { 3 } + 11 x ^ { 2 } y - 5 x y ^ { 2 } + 2 y ^ { 3 }$

Question 58

Multiply the monomial and the polynomial. Assume any variable exponents represent whole numbers.
$$4 x ^ { 2 } y \left( - 4 x ^ { 2 } y ^ { 4 } - 8 x y ^ { 3 } + 6 \right)$$

A) $- 16 x ^ { 4 } y ^ { 5 } - 32 x ^ { 3 } y ^ { 4 } + 24 x ^ { 2 } y$
B) $- 16 x ^ { 4 } y ^ { 5 } - 32 x ^ { 3 } y ^ { 4 } + 24$
C) $- 16 x ^ { 4 } y ^ { 5 } + 32 x ^ { 3 } y ^ { 4 } - 24 x ^ { 2 } y$
D) $- 16 x ^ { 2 } y ^ { 5 } - 32 x ^ { 3 } y ^ { 4 } + 24 x ^ { 2 } y$

Question 59

Subtract the polynomials. Assume all variable exponents represent whole numbers.
Subtract $5 a ^ { 2 } b ^ { 4 } + 8 a b ^ { 2 } - a b$ from $- 9 a ^ { 2 } b ^ { 4 } + 4 a b ^ { 2 } + 7 a b$

A) $- 14 a ^ { 2 } b ^ { 4 } + 4 a b ^ { 2 } + 6 a b$
B) $- 4 a ^ { 2 } b ^ { 4 } + 12 a b ^ { 2 } + 6 a b$
C) $14 a ^ { 2 } b ^ { 4 } + 4 a b ^ { 2 } - 8 a b$
D) $- 14 a ^ { 2 } b ^ { 4 } - 4 a b ^ { 2 } + 8 a b$

Question 60

Subtract the polynomials. Assume all variable exponents represent whole numbers.
$$\left( 2 x ^ { 2 n } - 7 x ^ { n } - 19 \right) - \left( 9 x ^ { 2 n } - 5 x ^ { n } + 13 \right)$$

A) $- 7 x ^ { 2 n } - 2 x ^ { n } - 6$
B) $- 7 x ^ { 2 n } + 2 x ^ { n } - 6$
C) $- 7 x ^ { 2 n } - 2 x ^ { n } - 32$
D) $- 7 x ^ { 4 n } - 2 x ^ { 2 n } - 32$

Question 61

Use the FOIL method to multiply the binomials. Assume any variable exponents represent whole numbers.
$$( 3 x y + 5 ) ( 4 x y + 9 )$$

A) $12 x ^ { 2 } y ^ { 2 } + 47 x y + 14$
B) $12 x ^ { 2 } y ^ { 2 } + 27 x y + 45$
C) $12 x ^ { 2 } y ^ { 2 } + 47 x y + 45$
D) $7 x ^ { 2 } y ^ { 2 } + 47 x y + 45$

Question 62

Use the FOIL method to multiply the binomials. Assume any variable exponents represent whole numbers.
$$( 9 x - y ) ( 7 x - 12 y )$$

A) $16 x ^ { 2 } - 115 x y + 12 y ^ { 2 }$
B) $63 x ^ { 2 } - 115 x y - 12 y ^ { 2 }$
C) $63 x ^ { 2 } + 115 x y + 12 y ^ { 2 }$
D) $63 x ^ { 2 } - 115 x y + 12 y ^ { 2 }$

Question 63

Find the product. Assume all variable exponents represent whole numbers.
$$\left( x ^ { 2 } + x + 3 \right) \left( x ^ { 2 } + x + 6 \right)$$

A) $x ^ { 4 } + x ^ { 3 } + 9 x ^ { 2 } + 9 x + 18$
B) $x ^ { 4 } + x ^ { 3 } - 8 x ^ { 2 } - 9 x + 18$
C) $x ^ { 4 } + 2 x ^ { 3 } + 10 x ^ { 2 } + 9 x + 18$
D) $x ^ { 4 } + 2 x ^ { 3 } - 9 x ^ { 2 } - 3 x + 18$

Question 64

Find the product. Assume all variable exponents represent whole numbers.
$$( p - q ) \left( p ^ { 2 } + p q + q ^ { 2 } \right)$$

A) $p ^ { 3 } - q ^ { 3 }$
B) $p ^ { 3 } - 2 p ^ { 2 } q - 2 p q ^ { 2 } - q ^ { 3 }$
C) $p ^ { 3 } + 2 p ^ { 2 } q + 2 p q ^ { 2 } - q ^ { 3 }$
D) $\mathrm { p } ^ { 3 } + \mathrm { q } ^ { 3 }$

Question 65

Use the FOIL method to multiply the binomials. Assume any variable exponents represent whole numbers.
$( x - 10 ) \left( x ^ { 2 } - 12 \right)$

A) $x ^ { 3 } - 22 x + 120$
B) $x ^ { 3 } - 22 x ^ { 2 } + 120$
C) $x ^ { 3 } - 10 x ^ { 2 } - 12 x + 120$
D) $x ^ { 3 } + 10 x ^ { 2 } + 12 x + 120$

Question 66

Solve the problem.
Find the area of the rectangle by multiplying the length and the width of the large rectangle using the FOIL method.

A) $x ^ { 2 } + 63$
B) $x ^ { 2 } + 16 x$
C) $x ^ { 2 } + 16 x + 63$
D) $x ^ { 2 } + 32 x + 63$

Question 67

Find the product. Assume all variable exponents represent whole numbers.
$$( x + y ) \left( x ^ { 2 } - 6 x y - y ^ { 2 } \right)$$

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

Question 68

Solve the problem.
Find the area of the rectangle by multiplying the length and the width of the large rectangle using the FOIL method.

A) $4 x ^ { 2 } + 39 x$
B) $4 x ^ { 2 } + 32 x + 56$
C) $4 x ^ { 2 } + 7 x + 56$
D) $4 \mathrm { x } ^ { 2 } + 39 \mathrm { x } + 56$

Question 69

Find the product. Assume all variable exponents represent whole numbers.
$$\left( 2 x ^ { 2 } + 5 x - 4 \right) \left( x ^ { 2 } + 4 x - 4 \right)$$

A) $2 x ^ { 4 } + 8 x ^ { 3 } + 12 x ^ { 2 } - 36 x + 16$
B) $2 x ^ { 4 } + 13 x ^ { 3 } + 12 x ^ { 2 } - 36 x + 16$
C) $2 x ^ { 4 } + 13 x ^ { 3 } + 8 x ^ { 2 } - 36 x + 16$
D) $2 x ^ { 4 } + 8 x ^ { 3 } + 8 x ^ { 2 } - 36 x + 16$

Question 70

Use the FOIL method to multiply the binomials. Assume any variable exponents represent whole numbers.
$$\left( 4 x ^ { n } + 11 y ^ { n } \right) \left( x ^ { n } + 9 y ^ { n } \right)$$

A) $4 x ^ { 2 n } + 47 x ^ { n } y ^ { n } - 99 y ^ { 2 n }$
B) $4 x ^ { 2 n } + 47 x ^ { n } y ^ { n } + 99 y ^ { 2 n }$
C) $4 x ^ { n } + 2 + 47 x ^ { n } y ^ { n } + 99 y n + 2$
D) $4 \mathrm { x } ^ { \mathrm { n } } + 47 \mathrm { x } ^ { \mathrm { n } } \mathrm { y } ^ { \mathrm { n } } + 99 \mathrm { y } ^ { \mathrm { n } }$

Question 71

Use the FOIL method to multiply the binomials. Assume any variable exponents represent whole numbers.
$$( 5 x - 2 ) ( 3 x - 4 )$$

A) $15 x ^ { 2 } - 26 x + 8$
B) $15 x ^ { 2 } - 26 x - 26$
C) $8 x ^ { 2 } - 26 x + 8$
D) $8 x ^ { 2 } - 26 x - 26$

Question 72

Use the FOIL method to multiply the binomials. Assume any variable exponents represent whole numbers.
$$\left( 3 x ^ { 3 } - 6 \right) \left( x ^ { 2 } - 5 \right)$$

A) $3 x ^ { 5 } - 21 x ^ { 3 } + 30$
B) $3 x ^ { 5 } - 15 x ^ { 3 } - 6 x ^ { 2 } - 30$
C) $3 x ^ { 5 } - 15 x ^ { 3 } - 6 x ^ { 2 } + 30$
D) $4 x ^ { 5 } - 8 x ^ { 3 } - 7 x ^ { 2 } + 11$

Question 73

Solve the problem.
Write a polynomial that represents the volume of the open box.

A) $45 x + 154 x ^ { 2 } + 121 x ^ { 3 }$
B) $45 x - 154 x ^ { 2 } + 11 x ^ { 3 }$
C) $45 - 154 x + 121 x ^ { 2 }$
D) $45 x - 154 x ^ { 2 } + 121 x ^ { 3 }$

Question 74

Find the product. Assume all variable exponents represent whole numbers.
$$( x y - 7 ) \left( x ^ { 2 } y ^ { 2 } + 2 x y + 6 \right)$$

A) $x ^ { 3 } y ^ { 3 } + 2 x ^ { 2 } y ^ { 2 } + 6 x y$
B) $x ^ { 3 } y ^ { 3 } + 9 x ^ { 2 } y ^ { 2 } + 20 x y + 42$
C) $7 x ^ { 3 } y ^ { 3 } - 14 x ^ { 2 } y ^ { 2 } - 42 x y$
D) $x ^ { 3 } y ^ { 3 } - 5 x ^ { 2 } y ^ { 2 } - 8 x y - 42$

Question 75

Use the FOIL method to multiply the binomials. Assume any variable exponents represent whole numbers.
$$( x + 7 y ) ( x + 2 y )$$

A) $x ^ { 2 } + 9 x y + 14 y ^ { 2 }$
B) $x + 9 x y + 14 y$
C) $x ^ { 2 } + 6 x y + 14 y ^ { 2 }$
D) $x ^ { 2 } + 9 x y + 9 y ^ { 2 }$

Question 76

Use the FOIL method to multiply the binomials. Assume any variable exponents represent whole numbers.
$$( x + 4 ) ( x + 1 )$$

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

Question 77

Use the FOIL method to multiply the binomials. Assume any variable exponents represent whole numbers.
$$( 8 x + 12 y ) ( 8 x - 10 y )$$

A) $64 x ^ { 2 } + 16 x y - 120 y ^ { 2 }$
B) $64 x ^ { 2 } + 96 x y - 120 y ^ { 2 }$
C) $64 x ^ { 2 } + 16 x y + 16 y ^ { 2 }$
D) $64 x ^ { 2 } - 80 x y - 120 y ^ { 2 }$

Question 78

Find the product. Assume all variable exponents represent whole numbers.
$$( x - 4 ) \left( x ^ { 2 } + 4 x + 16 \right)$$

A) $x ^ { 3 } - 64$
B) $x ^ { 3 } + 64$
C) $x ^ { 3 } + 8 x ^ { 2 } + 8 x - 64$
D) $x ^ { 3 } - 8 x ^ { 2 } - 8 x - 64$

Question 79

Solve the problem.
Write a polynomial that represents the area of the shaded region.

A) $67 x ^ { 2 } - 9$
B) $61 x ^ { 2 } + 9$
C) $64 x ^ { 2 } - 3 x - 9$
D) $61 \mathrm { x } ^ { 2 } - 9$

Question 80

Use the FOIL method to multiply the binomials. Assume any variable exponents represent whole numbers.
$$( x - 10 y ) ( 4 x - 3 y )$$

A) $4 x ^ { 2 } - 43 x y - 30 y ^ { 2 }$
B) $4 x ^ { 2 } - 43 x y + 13 y ^ { 2 }$
C) $4 x ^ { 2 } - 43 x y + 30 y ^ { 2 }$
D) $4 x ^ { 2 } + 43 x y + 30 y ^ { 2 }$