EXAMPLE 4 Rewrite polynomials Divide 5y + y 2 + 4 by 2 + y. Rewrite polynomials. Multiply y and y + 2. y 2 + 2y Subtract y 2 + 2y. Bring down 4. 3y + 4.

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EXAMPLE 4 Rewrite polynomials Divide 5y + y by 2 + y. Rewrite polynomials. Multiply y and y + 2. y 2 + 2y Subtract y 2 + 2y. Bring down 4. 3y + 4 Multiply 3 and y y + 6 Subtract 3y + 6. – 2 y + 2 y 2 + 5y + 4 y ANSWER (5y + y 2 + 4) (2 + y) = y y + 2 – 2 + 3

EXAMPLE 5 Insert missing terms Divide m 2 by – 1 + 2m. Rewrite polynomials, Insert missing term. 2m2m 2m – 1 4m 2 + 0m + 13 Multiply 2m and 2m – 1. 4m 2 – 2m Subtract 4m 2 – 2m. Bring down 13. 2m + 13 Multiply 1 and 2m – 1. 2m – 1 Subtract 2m – ANSWER (13 + 4m 2 ) (– 1 + 2m) = 2m m –

EXAMPLE 6 Rewrite and graph a rational function Graph y = 2x – 1 x – 2 SOLUTION STEP 1 + x – h a Rewrite the rational function in the form y = k.k. x – 22x – 1 2x – So, y = + 2. x – 2 3

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 + 4m 2 ) (5 + 2m) ANSWER 2m – 1+ 2m + 5 – 2 6. Divide: (n 2 – 6) (– 3 + n) n ANSWER n – 3 3

Graph y = 3x + 1 x + 1 GUIDED PRACTICE for Examples 4, 5, and 6

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