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Prealgebra

Julie Miller, Molly O’Neill, Nancy Hyde

Chapter 10

Exponents and Polynomials - all with Video Answers

Educators

JT

Section 1

Addition and Subtraction of Polynomials

00:44

Problem 1

List three benefits of successfully completing this course.

David Collins
David Collins
Numerade Educator
00:57

Problem 2

Define the key terms.
a. Binomial
b. Coefficient
c. Degree
d. Descending order
e. Monomial
Binomial
b. Coefficient
c. Degree
d. Descending order
lonomial
eacher
g. Term
h. Trinomial
f. Polynomial
g. Term
h. Trinomial

Prashansha Kaushik
Prashansha Kaushik
Numerade Educator
00:18

Problem 3

Complete the table. Write the polynomial in descending order. Determine the degree of the
polynomial, and categorize the polynomial as a monomial, a binomial, or trinomial.
$$\begin{array}{|l|l|l|l|l|}\hline & & \text { Descending Order } & \text { Degree } & \text { Category } \\
\hline \text { 3. } & -7+2 x^{4} & & \\\hline\end{array}$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:22

Problem 4

Complete the table. Write the polynomial in descending order. Determine the degree of the
polynomial, and categorize the polynomial as a monomial, a binomial, or trinomial.
$$\begin{array}{l|l|l|l|l}\hline & & \text { Descending Order } & \text { Degree } & \text { Category } \\\hline \text { 4. } & 3+4 p^{3} & & & \\\hline\end{array}$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:28

Problem 5

Complete the table. Write the polynomial in descending order. Determine the degree of the
polynomial, and categorize the polynomial as a monomial, a binomial, or trinomial.
$$\begin{array}{l|l|l|l|l}\hline & & \text { Descending Order } & \text { Degree } & \text { Category } \\
\hline \text { 5. } & 2 y^{3}-4 y^{5}+9 y & & \\\hline\end{array}$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:24

Problem 6

Complete the table. Write the polynomial in descending order. Determine the degree of the
polynomial, and categorize the polynomial as a monomial, a binomial, or trinomial.
$$\begin{array}{l|l|l|l|l}\hline & & \text { Descending Order } & \text { Degree } & \text { Category } \\
\hline 6 . & 7 m-6 m^{4}+5 m^{3} & & \\\hline\end{array}$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:18

Problem 7

Complete the table. Write the polynomial in descending order. Determine the degree of the
polynomial, and categorize the polynomial as a monomial, a binomial, or trinomial.
$$\begin{array}{l|l|l|l|l}\hline & & \text { Descending Order } & \text { Degree } & \text { Category } \\
\hline 7 . & 12 z^{7} & & \\\hline\end{array}$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:17

Problem 8

Complete the table. Write the polynomial in descending order. Determine the degree of the
polynomial, and categorize the polynomial as a monomial, a binomial, or trinomial.
$$\begin{array}{l|l|l|l|l}\hline & & \text { Descending Order } & \text { Degree } & \text { Category } \\
\hline \text { 8. } & 11 n^{2} & \\\hline\end{array}$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:16

Problem 9

Complete the table. Write the polynomial in descending order. Determine the degree of the
polynomial, and categorize the polynomial as a monomial, a binomial, or trinomial.
$$\begin{array}{l|l|l|l|l}\hline & & \text { Descending Order } & \text { Degree } & \text { Category } \\\hline \text { 9. } & 9 k-4 & & \\\hline\end{array}$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:16

Problem 10

Complete the table. Write the polynomial in descending order. Determine the degree of the
polynomial, and categorize the polynomial as a monomial, a binomial, or trinomial.
$$\begin{array}{l|l|l|l|l}\hline & & \text { Descending Order } & \text { Degree } & \text { Category } \\
\hline 10 . & 13 w+8 & & \\\hline\end{array}$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:11

Problem 11

Determine if the term is a monomial.
$$18 p^{2} q$$

Julie Silva
Julie Silva
Numerade Educator
00:11

Problem 12

Determine if the term is a monomial.
$$-4 a^{9} c$$

Julie Silva
Julie Silva
Numerade Educator
00:10

Problem 13

Determine if the term is a monomial.
$$\frac{7 a^{2}}{d^{3}}$$

Julie Silva
Julie Silva
Numerade Educator
00:27

Problem 14

Determine if the term is a monomial.
$$\frac{15 n^{4}}{m}$$

Julie Silva
Julie Silva
Numerade Educator
00:24

Problem 15

Identify the coefficient of each term.
a. $-5 x^{2} y$
b. $12 a^{5}$
c. 6
d. $w z$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:21

Problem 16

Identify the coefficient of each term.
a. $9 a b$
b. $-4 y^{7}$
c. $-8$
d. $c d$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:16

Problem 17

Determine if the terms are like terms.
$$-6 x \quad and\quad 6 x^{2}$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:17

Problem 18

Determine if the terms are like terms.
$$9 y^{4} \text { and } 9 y^{2}$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:18

Problem 19

Determine if the terms are like terms.
$$-2 x^{3} y \text { and } 5 x^{3} y$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:25

Problem 20

Determine if the terms are like terms.
$$a^{2} b^{4} \text { and }-4 a^{2} b^{4}$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:14

Problem 21

Combine like terms.
$$-8 p^{2}-2 p^{2}$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:16

Problem 22

Combine like terms.
$$-16 w^{4}-2 w^{4}$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:19

Problem 23

Combine like terms.
$$12 y^{3}-4 y^{3}+6 y^{3}$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:24

Problem 24

Combine like terms.
$$9 z^{2}+11 z^{2}-8 z^{2}$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:28

Problem 25

Combine like terms.
$$2.4 x^{4}-1.6 x^{4}+5.1 x^{4}$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:31

Problem 26

Combine like terms.
$$-6.8 w^{3}+2.1 w^{3}-1.5 w^{3}$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:21

Problem 27

Add the polynomials.
$$(4 t-8)+(3 t+11)$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:25

Problem 28

Add the polynomials.
$$(14 m-9)+(12 m+2)$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:30

Problem 29

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

Grace Muhihu
Grace Muhihu
Numerade Educator
00:35

Problem 30

Add the polynomials.
$$\left(15 x^{4}+10 x^{3}\right)+\left(-6 x^{4}+9 x^{3}\right)$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:50

Problem 31

Add the polynomials.
$$\left(-6 z^{3}-2 z^{2}+\frac{3}{4}\right)+\left(4 z^{3}+10 z^{2}-\frac{1}{3}\right)$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:42

Problem 32

Add the polynomials.
$$\left(-w^{2}+6 w-\frac{5}{4}\right)+\left(9 w^{2}-5 w+\frac{1}{2}\right)$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:50

Problem 33

Add the polynomials.
$$\left(8 x^{2} y+2 x y-3 x y^{2}\right)+\left(-9 x^{2} y-x y+6 x y^{2}\right)$$

Grace Muhihu
Grace Muhihu
Numerade Educator
01:01

Problem 34

Add the polynomials.
$$\left(4 a^{3} b^{2}+2 a^{2} b^{2}-9 a b^{2}\right)+\left(6 a^{3} b^{2}-11 a^{2} b^{2}+4 a b^{2}\right)$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:27

Problem 35

Add the polynomials.
$$\begin{array}{r}18 x^{3}-x^{2}+9 x-3 \\+5 x^{3}+6 x^{2}-14 x+11 \\\hline\end{array}$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:29

Problem 36

Add the polynomials.
$$\begin{array}{r}14 z^{3}+7 z^{2}-13 z+2 \\+6 z^{3}-9 z^{2}+10 z-20 \\\hline\end{array}$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:51

Problem 37

Add the polynomials.
$$\begin{aligned}&6 y^{3} \quad+8 y+5\\&+\left(-9 y^{3}+16 y^{2}-3\right)\end{aligned}$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:51

Problem 38

Add the polynomials.
$$\begin{aligned}&12 p^{3}+7 p^{2} \quad-9\\&+\left(-p^{3} \quad-8 p-4\right)\end{aligned}$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:55

Problem 39

Add $\left(-12 x^{4}-2 x^{2}+6 x\right)$ to $\left(9 x^{4}+2 x^{3}+4 x\right)$.

Grace Muhihu
Grace Muhihu
Numerade Educator
00:51

Problem 40

$\operatorname{Add}\left(5 a^{3}+2 a-3\right)$ to $\left(6 a^{2}+9 a+7\right)$.

Grace Muhihu
Grace Muhihu
Numerade Educator
00:15

Problem 41

Write the opposite of the polynomial.
$$9 x^{2}-2 x-3$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:16

Problem 42

Write the opposite of the polynomial.
$$12 x^{3}+4 x^{2}-8$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:16

Problem 43

Write the opposite of the polynomial.
$$-1.3 y+z$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:20

Problem 44

Write the opposite of the polynomial.
$$2.4 m-5.1 n$$

Grace Muhihu
Grace Muhihu
Numerade Educator
01:05

Problem 45

Subtract the polynomials.
$$\left(9 p^{3}-4 p^{2}+2 p\right)-\left(2 p^{3}+6 p^{2}-3 p\right)$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:48

Problem 46

Subtract the polynomials.
$$\left(12 c^{2}+6 c-3\right)-\left(4 c^{2}-3 c+8\right)$$

Grace Muhihu
Grace Muhihu
Numerade Educator
01:21

Problem 47

Subtract the polynomials.
$$\left(-19 a^{5}-6 a^{3}+2 a^{2}+7\right)-\left(4 a^{5}+2 a^{3}+6 a^{2}-3\right)$$

Grace Muhihu
Grace Muhihu
Numerade Educator
01:32

Problem 48

Subtract the polynomials.
$$\left(-8 y^{4}+2 y^{2}-3 y+10\right)-\left(6 y^{4}+y^{3}+11 y-9\right)$$

Grace Muhihu
Grace Muhihu
Numerade Educator
01:47

Problem 49

Subtract the polynomials.
$$\left(2 a^{2} b^{2}-7 a b^{3}+6 a b-8 b^{3}\right)-\left(3 a^{2} b^{2}+9 a b-4 b^{3}\right)$$

Grace Muhihu
Grace Muhihu
Numerade Educator
01:15

Problem 50

Subtract the polynomials.
$$\left(2 m n^{3}+6 m^{2} n^{2}+9 m n^{2}-3 m n\right)-\left(5 m n^{3}-2 m^{2} n^{2}-7 m n\right)$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:21

Problem 51

Subtract the polynomials.
$$\begin{array}{r}5 x^{2}+9 x-6 \\-\left(3 x^{2}-2 x+1\right) \\\hline\end{array}$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:29

Problem 52

Subtract the polynomials.
$$\begin{array}{r}15 a^{3}-2 a^{2}+4 a \\-\left(2 a^{3}+6 a^{2}-12 a\right) \\\hline\end{array}$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:42

Problem 53

Subtract the polynomials.
CAN'T COPY THE QUESTION

Grace Muhihu
Grace Muhihu
Numerade Educator
01:00

Problem 54

For Exercises $45-54,$ subtract the polynomials.
$$\begin{array}{c}
9 m^{4}-2 m^{2}+6 m+8 \\
-\left(-4 m^{4}-5 m^{3} \quad-10 m\right. \\
\hline
\end{array}$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:34

Problem 55

Subtract $\left(9 x^{2}+16 x-4\right)$ from $\left(2 x^{2}-4 x-9\right)$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:39

Problem 56

Subtract $\left(-5 w^{2}+6 w-3\right)$ from $\left(11 w^{2}-20 w+4\right)$.

Grace Muhihu
Grace Muhihu
Numerade Educator
00:37

Problem 57

Evaluate the polynomial for the given values of the variable.
$t^{2}-6 t-1$
a. for $t=-2$
b. for $t=\frac{1}{4}$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:39

Problem 58

Evaluate the polynomial for the given values of the variable.
$x^{2}+x+2$
a. for $x=-10$
b. for $x=\frac{2}{5}$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:37

Problem 59

Evaluate the polynomial for the given values of the variable.
$y^{3}-y^{2}-1$
a. for $x=-2$
b. for $x=0.2$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:37

Problem 60

Evaluate the polynomial for the given values of the variable.
$3 c^{3}-c+8$
a. for $c=-1$
b. for $c=0.1$

Grace Muhihu
Grace Muhihu
Numerade Educator
01:09

Problem 61

The cost (in dollars) to rent a beach house for $x$ days is given by the polynomial $250+219 x$. (See Example 9.)
a. Evaluate the polynomial for $x=3$ and interpret the answer in the context of this problem.
b. Evaluate the polynomial for $x=14$ and interpret the answer in the context of this problem.

Oluwaseyitan Balogun
Oluwaseyitan Balogun
Numerade Educator
View

Problem 62

The cost (in dollars) for a speeding ticket is given by the polynomial $110+15 x .$ In this context, $x$ is the number of miles per hour a motorist travels over the speed limit.
a. Evaluate the polynomial for $x=15$ and interpret the answer in the context of this problem.
b. Evaluate the polynomial for $x=25$ and interpret the answer in the context of this problem.

JT
Johanna Tuggay
Numerade Educator
View

Problem 63

The cost (in dollars) to rent a car is given by the polynomial $29.99 x+0.40 y .$ In this context, $x$ is the number of days that the car is rented and $y$ is the number of miles driven.
a. Evaluate the polynomial for $x=3$ and $y=350 .$ Interpret the answer in the context of this problem.
b. Evaluate the polynomial for $x=7$ and $y=720 .$ Interpret the answer in the context of this problem.

JT
Johanna Tuggay
Numerade Educator
View

Problem 64

The cost (in dollars) for a cab ride is given by the polynomial $2+1.25 x+$ $0.25 y .$ In this context, $x$ is the number of miles driven and $y$ is the time in minutes for the ride.
a. Evaluate the polynomial for $x=10$ and $y=20 .$ Interpret the answer in the context of this problem.
b. Evaluate the polynomial for $x=22$ and $y=40 .$ Interpret the answer in the context of this problem.

JT
Johanna Tuggay
Numerade Educator
00:23

Problem 65

Write a polynomial that represents the perimeter of the region.
CAN'T COPY THE FIGURE

Grace Muhihu
Grace Muhihu
Numerade Educator
00:21

Problem 66

Write a polynomial that represents the perimeter of the region.
CAN'T COPY THE FIGURE

Grace Muhihu
Grace Muhihu
Numerade Educator
00:32

Problem 67

Write a polynomial that represents the perimeter of the region.
CAN'T COPY THE FIGURE

Grace Muhihu
Grace Muhihu
Numerade Educator
00:26

Problem 68

Write a polynomial that represents the perimeter of the region.
CAN'T COPY THE FIGURE

Grace Muhihu
Grace Muhihu
Numerade Educator
00:34

Problem 69

Find the missing polynomial. $(4 x+5)+(\quad)=2 x-1$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:36

Problem 70

Find the missing polynomial. $(9 y-3)+(\quad)=-4 y+7$.

Grace Muhihu
Grace Muhihu
Numerade Educator
00:56

Problem 71

Perform the indicated operations.
$$\left(2 x^{3}-5 x+8\right)-\left(4 x^{2}+2 x-3\right)+\left(-7 x^{3}+8 x^{2}\right)$$

Grace Muhihu
Grace Muhihu
Numerade Educator
01:05

Problem 72

Perform the indicated operations.
$$\left(-9 m^{4}-7 m^{2}+8\right)-\left(3 m^{4}+9 m^{3}-11\right)-\left(8 m^{3}+m^{2}-3\right)$$

Grace Muhihu
Grace Muhihu
Numerade Educator
01:11

Problem 73

Perform the indicated operations.
$$\left(-5 a^{2}-9 a^{3}+10 a^{4}\right)+\left(2 a^{3}-a^{4}\right)-\left(8 a+4 a^{3}+10 a^{4}\right)$$

Grace Muhihu
Grace Muhihu
Numerade Educator
01:12

Problem 74

Perform the indicated operations.
$$\left(-t+8 t^{3}-3 t^{4}\right)-\left(5 t+4 t^{4}+6 t^{5}\right)+\left(15 t^{3}+2 t^{4}+6 t^{5}\right)$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:32

Problem 75

Perform the indicated operations.
$$\left(1.2 x^{2}+3.5 x-9.6\right)+\left(2.9 x^{2}-6.7 x-3.5\right)$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:30

Problem 76

Perform the indicated operations.
$$\left(-5.1 y^{2}+4.8 y+2.3\right)+\left(-1.1 y^{2}-8.9 y+3.0\right)$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:49

Problem 77

Perform the indicated operations.
$$\left(-\frac{5}{4} t^{3}+\frac{1}{8} t+1\right)-\left(\frac{3}{2} t^{3}-\frac{1}{2} t+\frac{2}{3}\right)$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:49

Problem 78

Perform the indicated operations.
$$\left(\frac{7}{8} a-4 b-\frac{1}{2} c\right)-\left(-\frac{1}{4} a+\frac{1}{2} b+\frac{3}{8} c\right)$$

Grace Muhihu
Grace Muhihu
Numerade Educator
00:30

Problem 79

Write a binomial with degree 4.

Oluwaseyitan Balogun
Oluwaseyitan Balogun
Numerade Educator
00:30

Problem 80

Write a binomial with degree 5.

Oluwaseyitan Balogun
Oluwaseyitan Balogun
Numerade Educator
01:02

Problem 81

Write a trinomial with degree 2.

Ashley High
Ashley High
Numerade Educator
01:02

Problem 82

Write a trinomial with degree 6.

Ashley High
Ashley High
Numerade Educator