Introductory and Intermediate Algebra for College Students 4th

Robert Blitzer

Chapter 5

Exponents and Polynomials - all with Video Answers

Educators

Section 1

Adding and Subtracting Polynomials

Problem 1

identify each polynomial as a monomial, a binomial, or a trinomial. Give the degree of the polynomial.
$$3 x+7$$

James Kiss

James Kiss

Numerade Educator

Problem 2

identify each polynomial as a monomial, a binomial, or a trinomial. Give the degree of the polynomial.
$$5 x-2$$

James Kiss

Numerade Educator

Problem 3

identify each polynomial as a monomial, a binomial, or a trinomial. Give the degree of the polynomial.
$$x^{3}-2 x$$

James Kiss

Numerade Educator

Problem 4

identify each polynomial as a monomial, a binomial, or a trinomial. Give the degree of the polynomial.
$$x^{5}-7 x$$

James Kiss

Numerade Educator

Problem 5

identify each polynomial as a monomial, a binomial, or a trinomial. Give the degree of the polynomial.
$$8 x^{2}$$

James Kiss

Numerade Educator

Problem 6

identify each polynomial as a monomial, a binomial, or a trinomial. Give the degree of the polynomial.
$$10 x^{2}$$

James Kiss

Numerade Educator

Problem 7

identify each polynomial as a monomial, a binomial, or a trinomial. Give the degree of the polynomial.
$$5$$

James Kiss

Numerade Educator

Problem 8

identify each polynomial as a monomial, a binomial, or a trinomial. Give the degree of the polynomial.
$$9$$

James Kiss

Numerade Educator

Problem 9

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

James Kiss

Numerade Educator

Problem 10

identify each polynomial as a monomial, a binomial, or a trinomial. Give the degree of the polynomial.
$$x^{2}-9 x+2$$

James Kiss

Numerade Educator

Problem 11

identify each polynomial as a monomial, a binomial, or a trinomial. Give the degree of the polynomial.
$$7 y^{2}-9 y^{4}+5$$

James Kiss

Numerade Educator

Problem 12

identify each polynomial as a monomial, a binomial, or a trinomial. Give the degree of the polynomial.
$$3 y^{2}-14 y^{5}+6$$

James Kiss

Numerade Educator

Problem 13

identify each polynomial as a monomial, a binomial, or a trinomial. Give the degree of the polynomial.
$$15 x-7 x^{3}$$

James Kiss

Numerade Educator

Problem 14

identify each polynomial as a monomial, a binomial, or a trinomial. Give the degree of the polynomial.
$$9 x-5 x^{3}$$

James Kiss

Numerade Educator

Problem 15

identify each polynomial as a monomial, a binomial, or a trinomial. Give the degree of the polynomial.
$$-9 y^{23}$$

James Kiss

Numerade Educator

Problem 16

identify each polynomial as a monomial, a binomial, or a trinomial. Give the degree of the polynomial.
$$-11 y^{26}$$

James Kiss

Numerade Educator

Problem 17

add the polynomials.
$$(9 x+8)+(-17 x+5)$$

James Kiss

Numerade Educator

Problem 18

add the polynomials.
$$(8 x-5)+(-13 x+9)$$

James Kiss

Numerade Educator

Problem 19

add the polynomials.
$$\left(4 x^{2}+6 x-7\right)+\left(8 x^{2}+9 x-2\right)$$

James Kiss

Numerade Educator

Problem 20

add the polynomials.
$$\left(11 x^{2}+7 x-4\right)+\left(27 x^{2}+10 x-20\right)$$

James Kiss

Numerade Educator

Problem 21

add the polynomials.
$$\left(7 x^{2}-11 x\right)+\left(3 x^{2}-x\right)$$

James Kiss

Numerade Educator

Problem 22

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

James Kiss

Numerade Educator

Problem 23

add the polynomials.
$$\left(4 x^{2}-6 x+12\right)+\left(x^{2}+3 x+1\right)$$

James Kiss

Numerade Educator

Problem 24

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

James Kiss

Numerade Educator

Problem 25

add the polynomials.
$$\left(4 y^{3}+7 y-5\right)+\left(10 y^{2}-6 y+3\right)$$

James Kiss

Numerade Educator

Problem 26

add the polynomials.
$$\left(2 y^{3}+3 y+10\right)+\left(3 y^{2}+5 y-22\right)$$

James Kiss

Numerade Educator

Problem 27

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

James Kiss

Numerade Educator

Problem 28

add the polynomials.
$$\left(4 x^{3}+5 x+13\right)+\left(-4 x^{2}+22\right)$$

James Kiss

Numerade Educator

Problem 29

add the polynomials.
$$\left(4 y^{2}+8 y+11\right)+\left(-2 y^{3}+5 y+2\right)$$

James Kiss

Numerade Educator

Problem 30

add the polynomials.
$$\left(7 y^{3}+5 y-1\right)+\left(2 y^{2}-6 y+3\right)$$

James Kiss

Numerade Educator

Problem 31

add the polynomials.
$$\left(-2 y^{6}+3 y^{4}-y^{2}\right)+\left(-y^{6}+5 y^{4}+2 y^{2}\right)$$

James Kiss

Numerade Educator

Problem 32

add the polynomials.
$$\left(7 r^{4}+5 r^{2}+2 r\right)+\left(-18 r^{4}-5 r^{2}-r\right)$$

James Kiss

Numerade Educator

Problem 33

add the polynomials.
$$\left(9 x^{3}-x^{2}-x-\frac{1}{3}\right)+\left(x^{3}+x^{2}+x+\frac{4}{3}\right)$$

James Kiss

Numerade Educator

Problem 34

add the polynomials.
$$\left(12 x^{3}-x^{2}-x+\frac{4}{3}\right)+\left(x^{3}+x^{2}+x-\frac{1}{3}\right)$$

James Kiss

Numerade Educator

Problem 35

add the polynomials.
$$\begin{aligned}
&\left(\frac{1}{5} x^{4}+\frac{1}{3} x^{3}+\frac{3}{8} x^{2}+6\right)+
\left(-\frac{3}{5} x^{4}+\frac{2}{3} x^{3}-\frac{1}{2} x^{2}-6\right)
\end{aligned}$$

James Kiss

Numerade Educator

Problem 36

add the polynomials.
$$\begin{aligned}
&\left(\frac{2}{5} x^{4}+\frac{2}{3} x^{3}+\frac{5}{8} x^{2}+7\right)+\left(-\frac{4}{5} x^{4}+\frac{1}{3} x^{3}-\frac{1}{4} x^{2}-7\right)
\end{aligned}$$

James Kiss

Numerade Educator

Problem 37

add the polynomials.
$$\begin{aligned}
&\left(0.03 x^{5}-0.1 x^{3}+x+0.03\right)+\left(-0.02 x^{5}+x^{4}-0.7 x+0.3\right)
\end{aligned}$$

James Kiss

Numerade Educator

Problem 38

add the polynomials.
$$\begin{aligned}
&\left(0.06 x^{5}-0.2 x^{3}+x+0.05\right)+\left(-0.04 x^{5}+2 x^{4}-0.8 x+0.5\right)
\end{aligned}$$

James Kiss

Numerade Educator

Problem 39

use a vertical format to add the polynomials.
$$\begin{aligned}
&5 y^{3}-7 y^{2}\\
&6 y^{3}+4 y^{2}
\end{aligned}$$

James Kiss

Numerade Educator

Problem 40

use a vertical format to add the polynomials.
$$\begin{array}{r}
13 x^{4}-x^{2} \\
7 x^{4}+2 x^{2} \\
\hline
\end{array}$$

James Kiss

Numerade Educator

Problem 41

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

James Kiss

Numerade Educator

Problem 42

use a vertical format to add the polynomials.
$$\begin{array}{c}
7 x^{2}-5 x-6 \\
-9 x^{2}+4 x+6 \\
\hline
\end{array}$$

James Kiss

Numerade Educator

Problem 43

use a vertical format to add the polynomials.
$$\begin{array}{r}
\frac{1}{4} x^{4}-\frac{2}{3} x^{3}-5 \\
-\frac{1}{2} x^{4}+\frac{1}{5} x^{3}+4.7 \\
\hline
\end{array}$$

James Kiss

Numerade Educator

Problem 44

use a vertical format to add the polynomials.
$$\begin{array}{r}
\frac{1}{3} x^{9}-\frac{1}{5} x^{5}-2.7 \\
-\frac{3}{4} x^{9}+\frac{2}{3} x^{5}+1
\end{array}$$

James Kiss

Numerade Educator

Problem 45

use a vertical format to add the polynomials.
$$\begin{array}{r}
y^{3}+5 y^{2}-7 y-3 \\
-2 y^{3}+3 y^{2}+4 y-11 \\
\hline
\end{array}$$

James Kiss

Numerade Educator

Problem 46

use a vertical format to add the polynomials.
$$\begin{array}{c}
y^{3}+y^{2}-7 y+9 \\
-y^{3}-6 y^{2}-8 y+11
\end{array}$$

James Kiss

Numerade Educator

Problem 47

use a vertical format to add the polynomials.
$$\begin{array}{r}
4 x^{3}-6 x^{2}+5 x-7 \\
-9 x^{3} \quad-4 x+3 \\
\hline
\end{array}$$

James Kiss

Numerade Educator

Problem 48

use a vertical format to add the polynomials.
$$\begin{array}{r}
-4 y^{3}+6 y^{2}-8 y+11 \\
2 y^{3} \quad+9 y-3 \\
\hline
\end{array}$$

James Kiss

Numerade Educator

Problem 49

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

James Kiss

Numerade Educator

Problem 50

use a vertical format to add the polynomials.
$$\begin{array}{r}
7 y^{5}-3 y^{3}+y^{2} \\
2 y^{3}-y^{2}-4 y-3 \\
\hline
\end{array}$$

James Kiss

Numerade Educator

Problem 51

use a vertical format to add the polynomials.
$$\begin{array}{r}
7 x^{2}-9 x+3 \\
4 x^{2}+11 x-2 \\
-3 x^{2}+5 x-6 \\
\hline
\end{array}$$

James Kiss

Numerade Educator

Problem 52

use a vertical format to add the polynomials.
$$\begin{array}{r}
7 y^{2}-11 y-6 \\
8 y^{2}+3 y+4 \\
-9 y^{2}-5 y+2 \\
\hline
\end{array}$$

James Kiss

Numerade Educator

Problem 53

use a vertical format to add the polynomials.
$$\begin{aligned}
&1.2 x^{3}-3 x^{2}+9.1\\
&\begin{array}{r}
7.8 x^{3}-3.1 x^{2}+8 \\
1.2 x^{2}-6 \\
\hline
\end{array}
\end{aligned}$$

James Kiss

Numerade Educator

Problem 54

use a vertical format to add the polynomials.
$$\begin{aligned}
&7.9 x^{3}-6.8 x^{2}+3.3\\
&6.1 x^{3}-2.2 x^{2}+7\\
&4.3 x^{2}-5
\end{aligned}$$

James Kiss

Numerade Educator

Problem 55

subtract the polynomials.
$$(x-8)-(3 x+2)$$

James Kiss

Numerade Educator

Problem 56

subtract the polynomials.
$$(x-2)-(7 x+9)$$

James Kiss

Numerade Educator

Problem 57

subtract the polynomials.
$$\left(x^{2}-5 x-3\right)-\left(6 x^{2}+4 x+9\right)$$

James Kiss

Numerade Educator

Problem 58

subtract the polynomials.
$$\left(3 x^{2}-8 x-2\right)-\left(11 x^{2}+5 x+4\right)$$

James Kiss

Numerade Educator

Problem 59

subtract the polynomials.
$$\left(x^{2}-5 x\right)-\left(6 x^{2}-4 x\right)$$

James Kiss

Numerade Educator

Problem 60

subtract the polynomials.
$$\left(3 x^{2}-2 x\right)-\left(5 x^{2}-6 x\right)$$

James Kiss

Numerade Educator

Problem 61

subtract the polynomials.
$$\left(x^{2}-8 x-9\right)-\left(5 x^{2}-4 x-3\right)$$

James Kiss

Numerade Educator

Problem 62

subtract the polynomials.
$$\left(x^{2}-5 x+3\right)-\left(x^{2}-6 x-8\right)$$

James Kiss

Numerade Educator

Problem 63

subtract the polynomials.
$$(y-8)-(3 y-2)$$

James Kiss

Numerade Educator

Problem 64

subtract the polynomials.
$$(y-2)-(7 y-9)$$

James Kiss

Numerade Educator

Problem 65

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

James Kiss

Numerade Educator

Problem 66

subtract the polynomials.
$$\left(5 y^{3}+y^{2}-3 y-8\right)-\left(y^{2}-8 y+11\right)$$

James Kiss

Numerade Educator

Problem 67

subtract the polynomials.
$$\left(7 n^{3}-n^{7}-8\right)-\left(6 n^{3}-n^{7}-10\right)$$

James Kiss

Numerade Educator

Problem 68

subtract the polynomials.
$$\left(2 n^{2}-n^{7}-6\right)-\left(2 n^{3}-n^{7}-8\right)$$

James Kiss

Numerade Educator

Problem 69

subtract the polynomials.
$$\left(y^{6}-y^{3}\right)-\left(y^{2}-y\right)$$

James Kiss

Numerade Educator

Problem 70

subtract the polynomials.
$$\left(y^{5}-y^{3}\right)-\left(y^{4}-y^{2}\right)$$

James Kiss

Numerade Educator

Problem 71

subtract the polynomials.
$$\left(7 x^{4}+4 x^{2}+5 x\right)-\left(-19 x^{4}-5 x^{2}-x\right)$$

James Kiss

Numerade Educator

Problem 72

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

James Kiss

Numerade Educator

Problem 73

subtract the polynomials.
$$\left(\frac{3}{7} x^{3}-\frac{1}{5} x-\frac{1}{3}\right)-\left(-\frac{2}{7} x^{3}+\frac{1}{4} x-\frac{1}{3}\right)$$

James Kiss

Numerade Educator

Problem 74

subtract the polynomials.
$$\left(\frac{3}{8} x^{2}-\frac{1}{3} x-\frac{1}{4}\right)-\left(-\frac{1}{8} x^{2}+\frac{1}{2} x-\frac{1}{4}\right)$$

James Kiss

Numerade Educator

Problem 75

use a vertical format to subtract the polynomials.
$$\begin{array}{r}
7 x+1 \\
-(3 x-5) \\
\hline
\end{array}$$

James Kiss

Numerade Educator

Problem 76

use a vertical format to subtract the polynomials.
$$\begin{array}{r}
4 x+2 \\
-(3 x-5) \\
\hline
\end{array}$$

James Kiss

Numerade Educator

Problem 77

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

James Kiss

Numerade Educator

Problem 78

use a vertical format to subtract the polynomials.
$$\begin{array}{r}
9 y^{2}-6 \\
-\left(-5 y^{2}+2\right) \\
\hline
\end{array}$$

James Kiss

Numerade Educator

Problem 79

use a vertical format to subtract the polynomials.
$$\begin{aligned}
&7 y^{2}-5 y+2\\
&-\left(11 y^{2}+2 y-3\right)
\end{aligned}$$

James Kiss

Numerade Educator

Problem 80

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

James Kiss

Numerade Educator

Problem 81

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

James Kiss

Numerade Educator

Problem 82

use a vertical format to subtract the polynomials.
$$\begin{array}{r}
3 y^{4}-4 y^{2}+7 \\
-\left(-5 y^{4}-6 y^{2}-13\right) \\
\hline
\end{array}$$

James Kiss

Numerade Educator

Problem 83

use a vertical format to subtract the polynomials.
$$\begin{array}{r}
5 y^{3}+6 y^{2}-3 y+10 \\
-\left(6 y^{3}-2 y^{2}-4 y-4\right) \\
\hline
\end{array}$$

James Kiss

Numerade Educator

Problem 84

use a vertical format to subtract the polynomials.
$$\begin{array}{r}
4 y^{3}+5 y^{2}+7 y+11 \\
-\left(-5 y^{3}+6 y^{2}-9 y-3\right) \\
\hline
\end{array}$$

James Kiss

Numerade Educator

Problem 85

use a vertical format to subtract the polynomials.
$$\begin{aligned}
7 x^{4}-3 x^{3}+2 x^{2} & \\
-\left(\quad-x^{3}-x^{2}+x-2\right) & \\
-& 1
\end{aligned}$$

James Kiss

Numerade Educator

Problem 86

use a vertical format to subtract the polynomials.
$$\begin{array}{r}
5 y^{6}-3 y^{3}+2 y^{2} \\
-\left(\quad-y^{3}-y^{2}-y-1\right) \\
\hline
\end{array}$$

James Kiss

Numerade Educator

Problem 87

use a vertical format to subtract the polynomials.
$$\begin{array}{r}
0.07 x^{3}-0.01 x^{2}+0.02 x \\
-\left(0.02 x^{3}-0.03 x^{2}-\right. & x) \\
\hline
\end{array}$$

James Kiss

Numerade Educator

Problem 88

use a vertical format to subtract the polynomials.
$$\begin{aligned}
&0.04 x^{3}-0.03 x^{2}+0.05 x\\
&\frac{-\left(0.02 x^{3}-0.06 x^{2}-x\right)}{x}
\end{aligned}$$

James Kiss

Numerade Educator

Problem 89

Graph each equation in Exercises $89-94 .$ Find seven solutions in your table of values for each equation by using integers for $x$, starting with $-3$ and ending with 3
$$y=x^{2}$$

James Kiss

Numerade Educator

Problem 90

Graph each equation in Exercises $89-94 .$ Find seven solutions in your table of values for each equation by using integers for $x$, starting with $-3$ and ending with 3
$$y=x^{2}-2$$

James Kiss

Numerade Educator

Problem 91

Graph each equation in Exercises $89-94 .$ Find seven solutions in your table of values for each equation by using integers for $x$, starting with $-3$ and ending with 3
$$y=x^{2}+1$$

James Kiss

Numerade Educator

Problem 92

Graph each equation in Exercises $89-94 .$ Find seven solutions in your table of values for each equation by using integers for $x$, starting with $-3$ and ending with 3
$$y=x^{2}+2$$

James Kiss

Numerade Educator

Problem 93

Graph each equation in Exercises $89-94 .$ Find seven solutions in your table of values for each equation by using integers for $x$, starting with $-3$ and ending with 3
$$y=4-x^{2}$$

James Kiss

Numerade Educator

Problem 94

Graph each equation in Exercises $89-94 .$ Find seven solutions in your table of values for each equation by using integers for $x$, starting with $-3$ and ending with 3
$$y=9-x^{2}$$

James Kiss

Numerade Educator

Problem 95

perform the indicated operations.
$$\left[\left(4 x^{2}+7 x-5\right)-\left(2 x^{2}-10 x+3\right)\right]-\left(x^{2}+5 x-8\right)$$

James Kiss

Numerade Educator

Problem 96

perform the indicated operations.
$$\begin{aligned}
&\left[\left(10 x^{3}-5 x^{2}+4 x+3\right)-\left(-3 x^{3}-4 x^{2}+x\right)\right]-
\left(7 x^{3}-5 x+4\right)
\end{aligned}$$

James Kiss

Numerade Educator

Problem 97

perform the indicated operations.
$$\begin{aligned}
&\left[\left(4 y^{2}-3 y+8\right)-\left(5 y^{2}+7 y-4\right)\right]-\left[\left(8 y^{2}+5 y-7\right)+\left(-10 y^{2}+4 y+3\right)\right]
\end{aligned}$$

James Kiss

Numerade Educator

Problem 98

perform the indicated operations.
$$\begin{aligned}
&\left[\left(7 y^{2}-4 y+2\right)-\left(12 y^{2}+3 y-5\right)\right]-\left[\left(5 y^{2}-2 y-8\right)+\left(-7 y^{2}+10 y-13\right)\right]
\end{aligned}$$

James Kiss

Numerade Educator

Problem 99

Subtract $x^{3}-2 x^{2}+2$ from the sum of $4 x^{3}+x^{2}$ and $-x^{3}+7 x-3$

James Kiss

Numerade Educator

Problem 100

Subtract $-3 x^{3}-7 x+5$ from the sum of $2 x^{2}+4 x-7$ and $-5 x^{3}-2 x-3$

James Kiss

Numerade Educator

Problem 101

Subtract $-y^{2}+7 y^{3}$ from the difference between $-5+y^{2}+4 y^{3}$ and $-8-y+7 y^{3} .$ Express the answer in standard form.

Julie Silva

Numerade Educator

Problem 102

Subtract $-2 y^{2}+8 y^{3}$ from the difference between $-6+y^{2}+5 y^{3}$ and $-12-y+13 y^{3} .$ Express the answer in standard form.

Kelsey Holley

Numerade Educator

Problem 103

Here are polynomial models that describe the median annual income for men, $M,$ and for women, $W,$ who have completed $x$ years of education:
$$ \begin{array}{l} M=177 x^{2}+288 x+7075 \\ W=255 x^{2}-2956 x+24,336 \\ M=-18 x^{3}+923 x^{2}-9603 x+48,446 \\ W=17 x^{3}-450 x^{2}+6392 x-14,764 \end{array} $$
a. Use the equations defined by polynomials of degree 3 to find a mathematical model for $M-W$
b. According to the model in part (a), what is the difference in the median annual income between men and women with 14 years of education?
c. According to the data displayed by the graph, what is the actual difference in the median annual income between men and women with 14 years of education? Did the model in part (b) underestimate or overestimate this difference? By how much?

Joanna Quigley

Numerade Educator

Problem 104

Here are polynomial models that describe the median annual income for men, $M,$ and for women, $W,$ who have completed $x$ years of education:
$$ \begin{array}{l} M=177 x^{2}+288 x+7075 \\ W=255 x^{2}-2956 x+24,336 \\ M=-18 x^{3}+923 x^{2}-9603 x+48,446 \\ W=17 x^{3}-450 x^{2}+6392 x-14,764 \end{array} $$
a. Use the equations defined by polynomials of degree 3 to find a mathematical model for $M-W$
b. According to the model in part (a), what is the difference in the median annual income between men and women with 16 years of education?
c. According to the data displayed by the graph, what is the actual difference in the median annual income between men and women with 16 years of education? Did the model in part (b) underestimate or overestimate this difference? By how much?

Joanna Quigley

Numerade Educator

Problem 105

Here are polynomial models that describe the median annual income for men, $M,$ and for women, $W,$ who have completed $x$ years of education:
$$ \begin{array}{l} M=177 x^{2}+288 x+7075 \\ W=255 x^{2}-2956 x+24,336 \\ M=-18 x^{3}+923 x^{2}-9603 x+48,446 \\ W=17 x^{3}-450 x^{2}+6392 x-14,764 \end{array} $$
a. Use the equation defined by a polynomial of degree 2 to find the median annual income for a man with 16 years of education. Does this underestimate or overestimate the median income shown by the bar graph in the previous column? By how much?
b. Shown in a rectangular coordinate system are the graphs of the polynomial models of degree 2 that describe median annual income, by level of education. Identify your solution from part (a) as a point on the appropriate graph.
c. Use the appropriate graph in part (b) to estimate, to the nearest thousand dollars, the median annual income for a woman with 16 years of education.

Joanna Quigley

Numerade Educator

Problem 106

Here are polynomial models that describe the median annual income for men, $M,$ and for women, $W,$ who have completed $x$ years of education:
$$ \begin{array}{l} M=177 x^{2}+288 x+7075 \\ W=255 x^{2}-2956 x+24,336 \\ M=-18 x^{3}+923 x^{2}-9603 x+48,446 \\ W=17 x^{3}-450 x^{2}+6392 x-14,764 \end{array} $$
a. Use the equation defined by a polynomial of degree 2 to find the median annual income for a woman with 18 years of education. Does this underestimate or overestimate the median income shown by the bar graph in the previous column? By how much?
b. Shown in Exercise $105(b)$ are rectangular coordinate graphs of the polynomial models of degree 2 that describe median annual income, by level of education. Identify your solution from part (a) as a point on the appropriate graph.
c. Use the appropriate graph in Exercise $105(b)$ to estimate, to the nearest thousand dollars, the median annual income for a man with 18 years of education.

Joanna Quigley

Numerade Educator

Problem 107

What is a polynomial?

James Kiss

Numerade Educator

Problem 108

What is a monomial? Give an example with your explanation.

James Kiss

Numerade Educator

Problem 109

What is a binomial? Give an example with your explanation.

James Kiss

Numerade Educator

Problem 110

What is a trinomial? Give an example with your explanation.

James Kiss

Numerade Educator

Problem 111

What is the degree of a polynomial? Provide an example with your explanation.

James Kiss

Numerade Educator

Problem 112

Explain how to add polynomials.

James Kiss

Numerade Educator

Problem 113

Explain how to subtract polynomials.

James Kiss

Numerade Educator

Problem 114

determine whether each statement “makes sense” or “does not make sense” and explain your reasoning.
I add like monomials by adding both their coefficients and the exponents that appear on their common variable factor.

James Kiss

Numerade Educator

Problem 115

determine whether each statement “makes sense” or “does not make sense” and explain your reasoning.
By looking at the first term of a polynomial, I can determine its degree.

James Kiss

Numerade Educator

Problem 116

determine whether each statement “makes sense” or “does not make sense” and explain your reasoning.
As long as I understand how to add and subtract polynomials, I can select the format, horizontal or vertical, that works best for me.

James Kiss

Numerade Educator

Problem 117

determine whether each statement “makes sense” or “does not make sense” and explain your reasoning.
I used two points and a checkpoint to graph $y=x^{2}-4$

James Kiss

Numerade Educator

Problem 118

determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.
It is not possible to write a binomial with degree 0 .

James Kiss

Numerade Educator

Problem 119

determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.
$$\frac{1}{5 x^{2}}+\frac{1}{3 x} \text { is a binomial. }$$

James Kiss

Numerade Educator

Problem 120

determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.
$\left(2 x^{2}-8 x+6\right)-\left(x^{2}-3 x+5\right)=x^{2}-5 x+1$ for any
value of $x .$

James Kiss

Numerade Educator

Problem 121

determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.
In the polynomial $3 x^{2}-5 x+13,$ the coefficient of $x$ is 5

James Kiss

Numerade Educator

Problem 122

determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.
What polynomial must be subtracted from $5 x^{2}-2 x+1$ so that the difference is $8 x^{2}-x+3 ?$

James Kiss

Numerade Educator

Problem 123

determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.
The number of people who catch a cold $t$ weeks after January 1 is $5 t-3 t^{2}+t^{3}$ The number of people who recover $t$ weeks after January 1 is $t-t^{2}+\frac{1}{3} t^{3}$ Write a polynomial in standard form for the number of people who are still ill with a cold $t$ weeks after January 1

James Kiss

Numerade Educator

Problem 124

determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.
Explain why it is not possible to add two polynomials of degree 3 and get a polynomial of degree 4

James Kiss

Numerade Educator

Problem 125

Simplify: $(-10)(-7) \div(1-8)$

James Kiss

Numerade Educator

Problem 126

Subtract: $-4.6-(-10.2)$

James Kiss

Numerade Educator

Problem 128

will help you prepare for the material covered in the next section.
Find the missing exponent, designated by the question mark, in the final step.
$$
x^{3} \cdot x^{4}=(x \cdot x \cdot x) \cdot(x \cdot x \cdot x \cdot x)=x^{2}
$$

James Kiss

Numerade Educator

Problem 129

will help you prepare for the material covered in the next section.
Use the distributive property to multiply: $3 x(x+5)$

James Kiss

Numerade Educator

Problem 130

will help you prepare for the material covered in the next section.
Simplify: $x(x+2)+3(x+2)$

James Kiss

Numerade Educator