Beginning Algebra, 11th Edition

We use vertical subtraction in Section 5.7when we divide polynomials.

Subtracting Polynomials Vertically

Subtract by columns to find

Arrange like terms in columns.

Change all signs in the second row, and then add.

Change all signs.

Add. NOW TRY

Adding and Subtracting Polynomials with More Than

One Variable

Add or subtract as indicated.

(a)

Combine like terms.

(b)

NOW TRY

=-x^2 y+ 4 xy+ 3 y^2

= 2 x^2 y+ 3 xy+y^2 - 3 x^2 y+xy+ 2 y^2

12 x^2 y+ 3 xy+ y^22 - 13 x^2 y-xy- 2 y^22

= 7 a+ab

= 4 a+ 2 ab-b+ 3 a- ab+b

14 a+ 2 ab-b 2 + 13 a-ab+ b 2

EXAMPLE 9

12 y^3 + y^2 + 6 y- 11

- 2 y^3 + 7 y^2 + 4 y- 6

14 y^3 - 6 y^2 + 2 y- 5

2 y^3 - 7 y^2 - 4 y+ 6

14 y^3 - 6 y^2 + 2 y- 5

114 y^3 - 6 y^2 + 2 y- 52 - 12 y^3 - 7 y^2 - 4 y+ 62.

EXAMPLE 8

Be careful with signs.

The coefficient of xyis 1.

OBJECTIVE 6 Graph equations defined by polynomials of degree 2. In

Chapter 3,we introduced graphs of linear equations (which are actually polynomial

equations of degree 1). By plotting points selectively, we can graph polynomial equa-

tions of degree 2.

Graphing Equations Defined by Polynomials of Degree 2

Graph each equation.

(a)

Select values for x. Then find the corresponding y-values. Selecting gives

so the point is on the graph of (Recall that in an ordered pair such as

the x-value comes first and the y-value second.) We show some ordered pairs

that satisfy in the table with FIGURE 3on the next page. If we plot the ordered

pairs from the table on a coordinate system and draw a smooth curve through them,

we obtain the graph shown in FIGURE 3.

y=x^2

1 2, 4 2 ,

12 , 42 y= x^2.

y= x^2 = 22 = 4 ,

x= 2

y=x^2

EXAMPLE 10

NOW TRY

EXERCISE 8

Subtract by columns.

• 1 - 10 x^2 - 3 x+ 72

112 x^2 - 9 x+ 42

NOW TRY
EXERCISE 9
Subtract.

• 16 x^2 - 7 xy+ 2 y^22

14 x^2 - 2 xy+y^22

NOW TRY ANSWERS
8.
9.- 2 x^2 + 5 xy-y^2

22 x^2 - 6 x- 3

324 CHAPTER 5 Exponents and Polynomials

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