Beginning Algebra, 11th Edition

For each polynomial, determine the number of terms and name the coefficients of the terms.

See Example 1.

In each polynomial, add like terms whenever possible. Write the result in descending powers

of the variable. See Example 2.

For each polynomial, first simplify, if possible, and write it in descending powers of the vari-

able. Then give the degree of the resulting polynomial and tell whether it is a monomial,a

binomial,a trinomial,or none of these.See Example 3.

Find the value of each polynomial for (a ) and (b). See Example 4.

Add. See Example 5.

46. 47. 48.

49.

50. 12 r^5 + 11 r^4 - 7 r^3 - 2 r^2 and - 8 r^5 + 3 r^3 + 2 r^2

9 m^3 - 5 m^2 + 4 m- 8 and - 3 m^3 + 6 m^2 - 6

1

3 y

(^2) -^1
3 y+
2
5
1
2 x
(^2) -^1
3 x+
2
3
4
7 y
(^2) -^1
5 y+
7
9
2
3 x
(^2) +^1
5 x+
1
4 a 6
(^3) - 4 a (^2) - 4
3 x^2 + 2 x 8 y^3 - 4 y 2 m^2 - 2 m- 4
2 x^2 - 4 x - 5 y^3 + 3 y 3 m^2 + 5 m+ 6
2 x^5 - 4 x^4 + 5 x^3 - x^2 x^4 - 6 x^3 +x^2 - x

• 3 x^2 + 14 x- 2 - 2 x^2 + 5 x- 1

2 x^2 - 3 x- 5 x^2 + 5 x- 10

x= 2 x=- 1

0.8x^4 - 0.3x^4 - 0.5x^4 + 7 1.2t^3 - 0.9t^3 - 0.3t^3 + 9

4

5

r^6 +

1

5

r^6

5

3

x^4 -

2

3

x^4

5 m^4 - 3 m^2 + 6 m^4 - 7 m^36 p^5 + 4 p^3 - 8 p^5 + 10 p^2

6 x^4 - 9 x 7 t^3 - 3 t

• 4 xy^2 + 3 xy^2 - 2 xy^2 +xy^23 pr^5 - 8 pr^5 +pr^5 + 2 pr^5


• 4 p^7 + 8 p^7 + 5 p^9 - 3 a^8 + 4 a^8 - 3 a^2


• 3 x^5 + 3 x^5 - 5 x^56 x^3 - 9 x^3 + 10 x^3

9 y^2 + 1 - 19 y^22 0.2m^5 - 0.5m^2 - 0.9y+0.9y^2

• 3 m^5 + 5 m^5 - 4 y^3 + 3 y^32 r^5 + 1 - 3 r^52


• 19 r^2 - r 2 y^3 - y x+ 8 x^2 + 5 x^3 v- 2 v^3 - v^7

6 x^4 - 9 y^5 t^4 s^7

6 a^3 + 5 a^2 - 8

Subtract. See Example 8.

53. 54.

55. 56.

57.After reading Examples 5– 8,do you have a preference regarding horizontal or vertical

addition and subtraction of polynomials? Explain your answer.

58.Write a paragraph explaining how to add and subtract polynomials. Give an example

using addition.

• 3 m^3 + 5 m^2 - 2 m- 4 - 6 a^4 + a^3 - a^2 +a- 1

12 m^3 - 8 m^2 + 6 m+ 7 5 a^4 - 3 a^3 + 2 a^2 - a+ 6

8 x^4 + 3 x^2 - 3 x 7 y^5 + 5 y^3 + y^2

12 x^4 - x^2 + x 13 y^5 - y^3 - 8 y^2

2 y^3 + 8 y^28 t^3 - 6 t^2

5 y^3 - 3 y^2 - 6 t^3 + 4 t^2

326 CHAPTER 5 Exponents and Polynomials

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