# SOLUTION EXAMPLE 2 Divide a polynomial by a binomial Divide x 2 + 2x – 3 by x – 1. STEP 1 Divide the first term of x 2 + 2x – 3 by the first term of x.

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SOLUTION EXAMPLE 2 Divide a polynomial by a binomial Divide x 2 + 2x – 3 by x – 1. STEP 1 Divide the first term of x 2 + 2x – 3 by the first term of x – 1. Multiply x and x – 1. x x – 1x 2 + 2x – 3 x 2 – x 3x3x Subtract x 2 – x from x 2 + 2x. Think : x 2 x = ?

EXAMPLE 2 Divide a polynomial by a binomial Bring down –3. Then divide the first term of 3x – 3 by the first term of x – 1. + 3 3x – 3 0 Multiply 3 and x – 1. Subtract 3x – 3 from 3x – 3. STEP 2 Think : 3x x = ? ANSWER (x 2 + 2x – 3) (x – 1) = x + 3 x – 1x 2 + 2x – 3 x 2 – x 3x – 3 x

EXAMPLE 3 Divide a polynomial by a binomial Divide 2x 2 + 11x – 9 by 2x – 3. x 2x 2 –3x 2x – 3 2x 2 + 11x – 9 14x – 9 12 Multiply x and 2x – 3. Subtract 2x 2 – 3x. Bring down – 9. Multiply 7 and 2x – 3. Subtract 14x – 21. ANSWER (2x 2 + 11x – 9) (2x – 3) = x + 7 + 12 2x – 3 14x – 21 + 7

GUIDED PRACTICE for Examples 2 and 3 3. Divide: (a 2 + 3a – 4) (a + 1) SOLUTION STEP 1 Divide the first term of a 2 + 3a – 4 by the first term of a + 1. Multiply a and a + 1. a a + 1a 2 + 3a – 4 a 2 + a 2a2a Subtract a 2 + a from a 2 + 3a. Think : a 2 a = ?

GUIDED PRACTICE for Examples 2 and 3 Bring down – 4. Then divide the first term of 2a – 4 by the first term of a + 1. a + 1a 2 + 3a – 4 a a 2 + a 2a – 4 2a + 2 – 6 Multiply 2 and a + 1. Subtract 2a + 2 from 2a – 4. STEP 2 Think : 2a a = ? ANSWER (a 2 + 3a – 4) (a +1) = a + 2 + – 6 a + 1 + 2

GUIDED PRACTICE for Examples 2 and 3 4. Divide: (9b 2 + 6b + 8) (3b – 4) SOLUTION STEP 1 Divide the first term of 9b 2 + 6b + 8 by the first term of 3 b – 4. Multiply 3b and 3b – 4. 3b3b 3b – 49b 2 + 6b + 8 9b 2 – 12b 18b Subtract 3b 2 – 12b from 9b 2 + 6b. Think : 9b 2 3b = ?

GUIDED PRACTICE for Examples 2 and 3 Bring down 8. Then divide the first term of 18b +8 by the first term of 3b – 4. 9b 2 – 12b 3b – 49b 2 + 6b + 8 3b3b 18b + 8 18b – 24 32 Multiply 6 and 3b – 4. Subtract 18b – 24 from 18b + 8. STEP 2 Think : 18b 3b = ? ANSWER (9b 2 + 6b +8) (3b – 4) = 3b + 6 + 32 3b – 4 + 6

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