EXAMPLE 4 Rewrite polynomials

Divide 5y + y2 + 4 by 2 + y.

Rewrite polynomials.Multiply y and y + 2.y2 + 2ySubtract y2 + 2y. Bring down 4.3y + 4Multiply 3 and y + 2.3y + 6Subtract 3y + 6.– 2

y + 2 y2 + 5y + 4y

ANSWER

(5y + y2 + 4) (2 + y) = y + 3 + y + 2– 2

+ 3

EXAMPLE 5 Insert missing terms

Divide 13 + 4m2 by – 1 + 2m.

Rewrite polynomials, Insert missing term.2m

2m – 1 4m2 + 0m + 13Multiply 2m and 2m – 1.4m2 – 2mSubtract 4m2 – 2m. Bring down 13.2m + 13Multiply 1 and 2m – 1.2m – 1

Subtract 2m – 1.14

ANSWER

(13 + 4m2) (– 1 + 2m) = 2m + 1 + 2m – 114

+ 1

EXAMPLE 6 Rewrite and graph a rational function

Graph y = 2x – 1x – 2

SOLUTION

STEP 1

+x – ha

Rewrite the rational function inthe form y = k.

x – 2 2x – 12x – 4

3

2

So, y = + 2.x – 23

EXAMPLE 6 Rewrite and graph a rational function

STEP 2

Graph the function.

GUIDED PRACTICE for Examples 4, 5, and 6

5. Divide: (8m – 7 + 4m2) (5 + 2m)

ANSWER

2m – 1+ 2m + 5– 2

6. Divide: (n2 – 6) (– 3 + n)

n + 3 +

ANSWER

n – 3 3

Graph y = 3x + 1x + 1

GUIDED PRACTICE for Examples 4, 5, and 6