Intermediate Algebra for College Students

Robert Blitzer

Chapter 5

Polynomials, Polynomial Functions, and Factoring - all with Video Answers

Educators

Section 1

Introduction to Polynomials and Polynomial Functions

Problem 1

Determine the coefficient of each term, the degree of each term, the degree of the polynomial, the leading term, and the leading coefficient of the polynomial.
$$-x^{4}+x^{2}$$

Pammi E.

Pammi E.

Numerade Educator

Problem 2

Determine the coefficient of each term, the degree of each term, the degree of the polynomial, the leading term, and the leading coefficient of the polynomial.
$$x^{3}-4 x^{2}$$

Pammi E.

Numerade Educator

Problem 3

Determine the coefficient of each term, the degree of each term, the degree of the polynomial, the leading term, and the leading coefficient of the polynomial.
$$5 x^{3}+7 x^{2}-x+9$$

Pammi E.

Numerade Educator

Problem 4

Determine the coefficient of each term, the degree of each term, the degree of the polynomial, the leading term, and the leading coefficient of the polynomial.
$$11 x^{3}-6 x^{2}+x+3$$

Pammi E.

Numerade Educator

Problem 5

Determine the coefficient of each term, the degree of each term, the degree of the polynomial, the leading term, and the leading coefficient of the polynomial.
$$3 x^{2}-7 x^{4}-x+6$$

Pammi E.

Numerade Educator

Problem 6

Determine the coefficient of each term, the degree of each term, the degree of the polynomial, the leading term, and the leading coefficient of the polynomial.
$$2 x^{2}-9 x^{4}-x+5$$

Pammi E.

Numerade Educator

Problem 7

Determine the coefficient of each term, the degree of each term, the degree of the polynomial, the leading term, and the leading coefficient of the polynomial.
$$x^{3} y^{2}-5 x^{2} y^{7}+6 y^{2}-3$$

Pammi E.

Numerade Educator

Problem 8

Determine the coefficient of each term, the degree of each term, the degree of the polynomial, the leading term, and the leading coefficient of the polynomial.
$$12 x^{4} y-5 x^{3} y^{7}-x^{2}+4$$

Pammi E.

Numerade Educator

Problem 9

Determine the coefficient of each term, the degree of each term, the degree of the polynomial, the leading term, and the leading coefficient of the polynomial.
$$x^{5}+3 x^{2} y^{4}+7 x y+9 x-2$$

Pammi E.

Numerade Educator

Problem 10

Determine the coefficient of each term, the degree of each term, the degree of the polynomial, the leading term, and the leading coefficient of the polynomial.
$$3 x^{6}+4 x^{4} y^{4}-x^{3} y+4 x^{2}-5$$

Pammi E.

Numerade Educator

Problem 11

Let $$f(x)=x^{2}-5 x+6 \text { and } g(x)=2 x^{3}-x^{2}+4 x-1$$
Find the indicated function values.
$f(3)$

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Problem 12

Let $$f(x)=x^{2}-5 x+6 \text { and } g(x)=2 x^{3}-x^{2}+4 x-1$$
Find the indicated function values.
$f(4)$

Pammi E.

Numerade Educator

Problem 13

Let $$f(x)=x^{2}-5 x+6 \text { and } g(x)=2 x^{3}-x^{2}+4 x-1$$
Find the indicated function values.
$f(-1)$

Pammi E.

Numerade Educator

Problem 14

Let $$f(x)=x^{2}-5 x+6 \text { and } g(x)=2 x^{3}-x^{2}+4 x-1$$
Find the indicated function values.
$f(-2)$

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Problem 15

Let $$f(x)=x^{2}-5 x+6 \text { and } g(x)=2 x^{3}-x^{2}+4 x-1$$
Find the indicated function values.
$g(3)$

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Problem 16

Let $$f(x)=x^{2}-5 x+6 \text { and } g(x)=2 x^{3}-x^{2}+4 x-1$$
Find the indicated function values.
$g(2)$

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Problem 17

Let $$f(x)=x^{2}-5 x+6 \text { and } g(x)=2 x^{3}-x^{2}+4 x-1$$
Find the indicated function values.
$g(-2)$

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Problem 18

Let $$f(x)=x^{2}-5 x+6 \text { and } g(x)=2 x^{3}-x^{2}+4 x-1$$
Find the indicated function values.
$g(-3)$

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Problem 19

Let $$f(x)=x^{2}-5 x+6 \text { and } g(x)=2 x^{3}-x^{2}+4 x-1$$
Find the indicated function values.
$g(0)$

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Problem 20

Let $$f(x)=x^{2}-5 x+6 \text { and } g(x)=2 x^{3}-x^{2}+4 x-1$$
Find the indicated function values.
$f(0)$

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Problem 21

Identify which graphs are not those of polynomial functions.

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Problem 22

Identify which graphs are not those of polynomial functions.

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Problem 23

Identify which graphs are not those of polynomial functions.

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Problem 24

Identify which graphs are not those of polynomial functions.

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Problem 25

Use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function. Then use this end behavior to match the polynomial function with its graph. [The graphs are labeled (a) through (d).]
$f(x)=-x^{4}+x^{2}$

Karly W.

Numerade Educator

Problem 26

Use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function. Then use this end behavior to match the polynomial function with its graph. [The graphs are labeled (a) through (d).]
$f(x)=x^{3}-4 x^{2}$

Karly W.

Numerade Educator

Problem 27

Use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function. Then use this end behavior to match the polynomial function with its graph. [The graphs are labeled (a) through (d).]
$f(x)=x^{2}-6 x+9$

Jonathan S.

Numerade Educator

Problem 28

Use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function. Then use this end behavior to match the polynomial function with its graph. [The graphs are labeled (a) through (d).]
$f(x)=-x^{3}-x^{2}+5 x-3$

Karly W.

Numerade Educator

Problem 29

Add the polynomials. Assume that all variable exponents represent whole numbers.
$\left(-6 x^{3}+5 x^{2}-8 x+9\right)+\left(17 x^{3}+2 x^{2}-4 x-13\right)$

Pammi E.

Numerade Educator

Problem 30

Add the polynomials. Assume that all variable exponents represent whole numbers.
$\left(-7 x^{3}+6 x^{2}-11 x+13\right)+\left(19 x^{3}-11 x^{2}+7 x-17\right)$

Pammi E.

Numerade Educator

Problem 31

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

Pammi E.

Numerade Educator

Problem 32

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

Pammi E.

Numerade Educator

Problem 33

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

Pammi E.

Numerade Educator

Problem 34

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

Pammi E.

Numerade Educator

Problem 35

Add the polynomials. Assume that all variable exponents represent whole numbers.
$\left(5 x^{2} y+9 x y+12\right)+\left(-3 x^{2} y+6 x y+3\right)$

Pammi E.

Numerade Educator

Problem 36

Add the polynomials. Assume that all variable exponents represent whole numbers.
$\left(8 x^{2} y+12 x y+14\right)+\left(-2 x^{2} y+7 x y+4\right)$

Pammi E.

Numerade Educator

Problem 37

Add the polynomials. Assume that all variable exponents represent whole numbers.
$\left(9 x^{4} y^{2}-6 x^{2} y^{2}+3 x y\right)+\left(-18 x^{4} y^{2}-5 x^{2} y-x y\right)$

Pammi E.

Numerade Educator

Problem 38

Add the polynomials. Assume that all variable exponents represent whole numbers.
$\left(10 x^{4} y^{2}-3 x^{2} y^{2}+2 x y\right)+\left(-16 x^{4} y^{2}-4 x^{2} y-x y\right)$

Pammi E.

Numerade Educator

Problem 39

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

Pammi E.

Numerade Educator

Problem 40

Add the polynomials. Assume that all variable exponents represent whole numbers.
$\left(6 y^{2 n}+y^{n}+5\right)+\left(3 y^{2 n}-4 y^{n}-15\right)$

Pammi E.

Numerade Educator

Problem 41

Subtract the polynomials. Assume that all variable exponents represent whole numbers.
$\left(17 x^{3}-5 x^{2}+4 x-3\right)-\left(5 x^{3}-9 x^{2}-8 x+11\right)$

Pammi E.

Numerade Educator

Problem 42

Subtract the polynomials. Assume that all variable exponents represent whole numbers.
$\left(18 x^{3}-2 x^{2}-7 x+8\right)-\left(9 x^{3}-6 x^{2}-5 x+7\right)$

Pammi E.

Numerade Educator

Problem 43

Subtract the polynomials. Assume that all variable exponents represent whole numbers.
$\left(13 y^{5}+9 y^{4}-5 y^{2}+3 y+6\right)-\left(-9 y^{5}-7 y^{3}+8 y^{2}+11\right)$

Pammi E.

Numerade Educator

Problem 44

Subtract the polynomials. Assume that all variable exponents represent whole numbers.
$\left(12 y^{5}+7 y^{4}-3 y^{2}+6 y+7\right)-\left(-10 y^{5}-8 y^{3}+3 y^{2}+14\right)$

Pammi E.

Numerade Educator

Problem 45

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

Pammi E.

Numerade Educator

Problem 46

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

Pammi E.

Numerade Educator

Problem 47

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

Pammi E.

Numerade Educator

Problem 48

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

Pammi E.

Numerade Educator

Problem 49

Subtract the polynomials. Assume that all variable exponents represent whole numbers.
$\left(7 y^{2 n}+y^{n}-4\right)-\left(6 y^{2 n}-y^{n}-1\right)$

Pammi E.

Numerade Educator

Problem 50

Subtract the polynomials. Assume that all variable exponents represent whole numbers.
$\left(8 x^{2 n}+x^{n}-4\right)-\left(9 x^{2 n}-x^{n}-2\right)$

Pammi E.

Numerade Educator

Problem 51

Subtract $-5 a^{2} b^{4}-8 a b^{2}-a b$ from $3 a^{2} b^{4}-5 a b^{2}+7 a b$.

Pammi E.

Numerade Educator

Problem 52

Subtract $-7 a^{2} b^{4}-8 a b^{2}-a b$ from $13 a^{2} b^{4}-17 a b^{2}+a b$.

Pammi E.

Numerade Educator

Problem 53

Subtract $-4 x^{3}-x^{2} y+x y^{2}+3 y^{3}$ from $x^{3}+2 x^{2} y-y^{3}$

Pammi E.

Numerade Educator

Problem 54

Subtract $-6 x^{3}+x^{2} y-x y^{2}+2 y^{3}$ from $x^{3}+2 x y^{2}-y^{3}$.

Pammi E.

Numerade Educator

Problem 55

Add $6 x^{4}-5 x^{3}+2 x$ to the difference between $4 x^{3}+3 x^{2}-1$ and $x^{4}-2 x^{2}+7 x-3$

Pammi E.

Numerade Educator

Problem 56

Add $5 x^{4}-2 x^{3}+7 x$ to the difference between $2 x^{3}+5 x^{2}-3$ and $-x^{4}-x^{2}-x-1$

Pammi E.

Numerade Educator

Problem 57

Subtract $9 x^{2} y^{2}-3 x^{2}-5$ from the sum of $-6 x^{2} y^{2}-x^{2}-1$ and $5 x^{2} y^{2}+2 x^{2}-1$

Pammi E.

Numerade Educator

Problem 58

Subtract $6 x^{2} y^{3}-2 x^{2}-7$ from the sum of $-5 x^{2} y^{3}+3 x^{2}-4$ and $4 x^{2} y^{3}-2 x^{2}-6$

Pammi E.

Numerade Educator

Problem 59

Let $$\begin{array}{l}f(x)=-3 x^{3}-2 x^{2}-x+4 \\g(x)=x^{3}-x^{2}-5 x-4 \\h(x)=-2 x^{3}+5 x^{2}-4 x+1\end{array}$$
Find the indicated function, function value, or polynomial.
$(f-g)(x)$ and $(f-g)(-1)$

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Problem 60

Let $$\begin{array}{l}f(x)=-3 x^{3}-2 x^{2}-x+4 \\g(x)=x^{3}-x^{2}-5 x-4 \\h(x)=-2 x^{3}+5 x^{2}-4 x+1\end{array}$$
Find the indicated function, function value, or polynomial.
$(g-h)(x)$ and $(g-h)(-1)$

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Problem 61

Let $$\begin{array}{l}f(x)=-3 x^{3}-2 x^{2}-x+4 \\g(x)=x^{3}-x^{2}-5 x-4 \\h(x)=-2 x^{3}+5 x^{2}-4 x+1\end{array}$$
Find the indicated function, function value, or polynomial.
$(f+g-h)(x)$ and $(f+g-h)(-2)$

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Problem 62

Let $$\begin{array}{l}f(x)=-3 x^{3}-2 x^{2}-x+4 \\g(x)=x^{3}-x^{2}-5 x-4 \\h(x)=-2 x^{3}+5 x^{2}-4 x+1\end{array}$$
Find the indicated function, function value, or polynomial.
$(g+h-f)(x)$ and $(g+h-f)(-2)$

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Problem 63

Let $$\begin{array}{l}f(x)=-3 x^{3}-2 x^{2}-x+4 \\g(x)=x^{3}-x^{2}-5 x-4 \\h(x)=-2 x^{3}+5 x^{2}-4 x+1\end{array}$$
$2 f(x)-3 g(x)$

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Problem 64

Let $$\begin{array}{l}f(x)=-3 x^{3}-2 x^{2}-x+4 \\g(x)=x^{3}-x^{2}-5 x-4 \\h(x)=-2 x^{3}+5 x^{2}-4 x+1\end{array}$$
$-2 g(x)-3 h(x)$

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Problem 65

As we noted in the chapter opener, experts fear that without conservation efforts, tigers could disappear from the wild by 2022. Just one hundred years ago, there were at least 100,000 wild tigers. By $2010,$ the estimated world tiger population was $3200 .$ The bar graph shows the estimated world tiger population for selected years from 1970 through $2010 .$ Also shown is a polynomial function, with its graph, that models the data. Use this in formation to solve this.
a. Find and interpret $f(40)$. Identify this information as a point on the graph of $f$
b. Does $f(40)$ overestimate or underestimate the actual data shown by the bar graph? By how much?

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Problem 66

As we noted in the chapter opener, experts fear that without conservation efforts, tigers could disappear from the wild by 2022. Just one hundred years ago, there were at least 100,000 wild tigers. By $2010,$ the estimated world tiger population was $3200 .$ The bar graph shows the estimated world tiger population for selected years from 1970 through $2010 .$ Also shown is a polynomial function, with its graph, that models the data. Use this in formation to solve this.
a. Find and interpret $f(10)$. Identify this information as a point on the graph of $f$
b. Does $f(10)$ overestimate or underestimate the actual data shown by the bar graph? By how much?

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Problem 67

As we noted in the chapter opener, experts fear that without conservation efforts, tigers could disappear from the wild by 2022. Just one hundred years ago, there were at least 100,000 wild tigers. By $2010,$ the estimated world tiger population was $3200 .$ The bar graph shows the estimated world tiger population for selected years from 1970 through $2010 .$ Also shown is a polynomial function, with its graph, that models the data. Use this in formation to solve this.
Use the Leading Coefficient Test to determine the end behavior to the right for the graph of $f$. Will this function be useful in modeling the world tiger population if conservation efforts to save wild tigers fail? Explain your answer.

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Problem 68

As we noted in the chapter opener, experts fear that without conservation efforts, tigers could disappear from the wild by 2022. Just one hundred years ago, there were at least 100,000 wild tigers. By $2010,$ the estimated world tiger population was $3200 .$ The bar graph shows the estimated world tiger population for selected years from 1970 through $2010 .$ Also shown is a polynomial function, with its graph, that models the data. Use this in formation to solve this.
Use the Leading Coefficient Test to determine the end behavior to the right for the graph of $f$. Might this function be useful in modeling the world tiger population if conservation efforts to save wild tigers are successful? Explain your answer.

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Problem 69

The common cold is caused by a rhinovirus. After $x$ days of invasion by the viral particles, the number of particles in our bodies, $f(x)$, in billions, can be modeled by the polynomial function
$$f(x)=-0.75 x^{4}+3 x^{3}+5$$
Use the Leading Coefficient Test to determine the graph's end behavior to the right. What does this mean about the number of viral particles in our bodies over time?

Jonathan S.

Numerade Educator

Problem 70

The polynomial function
$$f(x)=-0.87 x^{3}+0.35 x^{2}+81.62 x+7684.94$$
models the number of thefts, $f(x),$ in thousands, in the United States $x$ years after $1987 .$ Will this function be useful in modeling the number of thefts over an extended period of time? Explain your answer.

Jonathan S.

Numerade Educator

Problem 71

A herd of 100 elk is introduced to a small island. The number of elk, $f(x),$ after $x$ years is modeled by the polynomial function
$$f(x)=-x^{4}+21 x^{2}+100$$
Use the Leading Coefficient Test to determine the graph's end behavior to the right. What does this mean about what will eventually happen to the elk population?

Jonathan S.

Numerade Educator

Problem 72

What is a polynomial?

James K.

Numerade Educator

Problem 73

Explain how to determine the degree of each term of a polynomial.

Jonathan S.

Numerade Educator

Problem 74

Explain how to determine the degree of a polynomial.

Jonathan S.

Numerade Educator

Problem 75

Explain how to determine the leading coefficient of a polynomial.

Jonathan S.

Numerade Educator

Problem 76

What is a polynomial function?

Yuou S.

Numerade Educator

Problem 77

What do we mean when we describe the graph of a polynomial function as smooth and continuous?

Yuou S.

Numerade Educator

Problem 78

What is meant by the end behavior of a polynomial function?

Yuou S.

Numerade Educator

Problem 79

Explain how to use the Leading Coefficient Test to determine the end behavior of a polynomial function.

Yuou S.

Numerade Educator

Problem 80

Why is a polynomial function of degree 3 with a negative leading coefficient not appropriate for modeling nonnegative real-world phenomena over a long period of time?

Jonathan S.

Numerade Educator

Problem 81

Explain how to add polynomials.

James K.

Numerade Educator

Problem 82

Explain how to subtract polynomials.

James K.

Numerade Educator

Problem 83

In a favorable habitat and without natural predators, a population of reindeer is introduced to an island preserve. The reindeer population $t$ years after their introduction is modeled by the polynomial function
$$f(t)=-0.125 t^{5}+3.125 t^{4}+4000$$
Discuss the growth and decline of the reindeer population. Describe the factors that might contribute to this population model.

Jonathan S.

Numerade Educator

Problem 84

Write a polynomial function that imitates the end behavior of each graph. The dashed portions of the graphs indicate that you should focus only on imitating the left and right end behavior of the graph. You can be flexible about what occurs between the left and right ends. Then use your graphing utility to graph the polynomial function and verify that you imitated the end behavior shown in the given graph.

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Problem 85

Write a polynomial function that imitates the end behavior of each graph. The dashed portions of the graphs indicate that you should focus only on imitating the left and right end behavior of the graph. You can be flexible about what occurs between the left and right ends. Then use your graphing utility to graph the polynomial function and verify that you imitated the end behavior shown in the given graph.

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Problem 86

Write a polynomial function that imitates the end behavior of each graph. The dashed portions of the graphs indicate that you should focus only on imitating the left and right end behavior of the graph. You can be flexible about what occurs between the left and right ends. Then use your graphing utility to graph the polynomial function and verify that you imitated the end behavior shown in the given graph.

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Problem 87

Write a polynomial function that imitates the end behavior of each graph. The dashed portions of the graphs indicate that you should focus only on imitating the left and right end behavior of the graph. You can be flexible about what occurs between the left and right ends. Then use your graphing utility to graph the polynomial function and verify that you imitated the end behavior shown in the given graph.

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Problem 88

Use a graphing utility with a viewing rectangle large enough to show end behavior to graph each polynomial function.
$f(x)=x^{3}+13 x^{2}+10 x-4$

Yuou S.

Numerade Educator

Problem 89

Use a graphing utility with a viewing rectangle large enough to show end behavior to graph each polynomial function.
$f(x)=-2 x^{3}+6 x^{2}+3 x-1$

Yuou S.

Numerade Educator

Problem 90

Use a graphing utility with a viewing rectangle large enough to show end behavior to graph each polynomial function.
$f(x)=-x^{5}+5 x^{4}-6 x^{3}+2 x+20$

Yuou S.

Numerade Educator

Problem 91

Use a graphing utility with a viewing rectangle large enough to show end behavior to graph each polynomial function.
$f(x)=-x^{5}+5 x^{4}-6 x^{3}+2 x+20$

Yuou S.

Numerade Educator

Problem 92

Use a graphing utility to graph f and $g$ in the same viewing rectangle. Then use the ZOOM OUT $\mid$ feature to show that $f$ and $g$ have identical end behavior.
$f(x)=x^{3}-6 x+1, \quad g(x)=x^{3}$

Yuou S.

Numerade Educator

Problem 93

Use a graphing utility to graph f and $g$ in the same viewing rectangle. Then use the ZOOM OUT $\mid$ feature to show that $f$ and $g$ have identical end behavior.
$f(x)=-x^{4}+2 x^{3}-6 x, \quad g(x)=-x^{4}$

Karly W.

Numerade Educator

Problem 94

Determine whether each statement makes sense or does not make sense, and explain your
reasoning.
Many English words have prefixes with meanings similar to those used to describe polynomials, such as monologue, binocular, and tricuspid.

Jonathan S.

Numerade Educator

Problem 95

Determine whether each statement makes sense or does not make sense, and explain your
reasoning.
I can determine a polynomial's leading coefficient by inspecting the coefficient of the first term.

Jonathan S.

Numerade Educator

Problem 96

Determine whether each statement makes sense or does not make sense, and explain your
reasoning.
When I'm trying to determine end behavior, it's the coefficient of the first term of a polynomial function written in standard form that I should inspect.

Jonathan S.

Numerade Educator

Problem 97

Determine whether each statement makes sense or does not make sense, and explain your
reasoning.
When I rearrange the terms of a polynomial, it's important that I move the sign in front of a term with that term.

Jonathan S.

Numerade Educator

Problem 98

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.
$4 x^{3}+7 x^{2}-5 x+\frac{2}{x}$ is a polynomial containing four terms.

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Problem 99

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.
If two polynomials of degree 2 are added, the sum must be a polynomial of degree 2 .

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Problem 100

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.
$\left(x^{2}-7 x\right)-\left(x^{2}-4 x\right)=-11 x$ for all values of $x$.

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Problem 101

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.
All terms of a polynomial are monomials.

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Problem 102

In Exercises $102-103,$ perform the indicated operations. Assume that exponents represent whole numbers. Perform the indicated operations. Assume that exponents represent whole numbers.
$\left(x^{2 n}-3 x^{n}+5\right)+\left(4 x^{2 n}-3 x^{n}-4\right)-\left(2 x^{2 n}-5 x^{n}-3\right)$

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Problem 103

Perform the indicated operations. Assume that exponents represent whole numbers.
$\left(y^{3 n}-7 y^{2 n}+3\right)-\left(-3 y^{3 n}-2 y^{2 n}-1\right)+\left(6 y^{3 n}-y^{2 n}+1\right)$

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Problem 104

From what polynomial must $4 x^{2}+2 x-3$ be subtracted to obtain $5 x^{2}-5 x+8 ?$

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Problem 105

Solve: $9(x-1)=1+3(x-2)$

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Problem 106

Graph: $2 x-3 y<-6$

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Problem 107

Write the point-slope form and slope-intercept form of equations of a line passing through the point (-2,5) and parallel to the line whose equation is $3 x-y=9$.

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Problem 108

Multiply: $\left(2 x^{3} y^{2}\right)\left(5 x^{4} y^{7}\right)$

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Problem 109

Use the distributive property to multiply: $2 x^{4}\left(8 x^{4}+3 x\right)$.

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Problem 110

Simplify and express the polynomial in standard form:
$$3 x\left(x^{2}+4 x+5\right)+7\left(x^{2}+4 x+5\right)$$

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