1. Algebra 11.7 Dividing Polynomials

2. 9x² 3x 18 3x 12x 3x Dividing a Polynomial by a Monomial Divide 9x² + 12x – 18 by 3x 9x² + 12x – 18 3x =+- 3 11 4 1 6 1. Divide out common factors. Numbers first. Variables next. 2. Rewrite in simplified form. =3x + 4 - 6 x

3. 28 Long Division with Numbers The algorithm now seems simple. 65828 Divide 658 by 28 Ask: how many 28’s in 65? About 2 2 Multiply 2 x 28 and subtract from 65 56 98 Ask: how many 28’s in 98?About 3 3 Multiply 3 x 28 and subtract from 98 84 14 Remainder is 14 Quotient: 23 + 14 Remainder Divisor = 23½

4. x + 3 Polynomial Long Division Polynomial long division uses the same process as with numbers. It is used to divide a polynomial by a binomial. 3x² + 7x - 12 x + 3 Divide 3x² + 7x – 12 by x + 3 Ask: how many x’s in 3x²? 3x Multiply 3x by x + 3 and subtract 3x² + 9x -2x - 12 Ask: how many x’s in -2x?-2 Multiply -2 by x + 3 and subtract -2x - 6 -6 Remainder is -6 Quotient: 3x - 2 -6 Remainder Divisor Change signs when subtracting! +

5. Let’s try one together. x² - 3x + 5 x + 2 Divide x²- 3x + 5 by x + 2 Ask: how many x’s in x²? x x Multiply x by x + 2 and subtract x² + 2x -5x + 5 Ask: how many x’s in -5x?-5 Multiply -5 by x + 2 and subtract -5x - 10 15 Remainder is 15 Quotient: Change signs when subtracting!

6. You try. x² + 2x + 4 x - 1 Divide x²+ 2x + 4 by x - 1 Ask: how many x’s in x²? x x Multiply x by x - 1 and subtract x² - x 3x + 4 Ask: how many x’s in 3x?3 + 3 Multiply 3 by x - 1 and subtract 3x - 3 7 Remainder is 7 Quotient: Change signs when subtracting!

7. Adding a Place-holding ZERO. 6x² + 0x - 11 x + 2 Divide 6x²- 11 by x + 2 Ask: how many x’s in 6x²? 6x Multiply 6x by x + 2 and subtract 6x² +12x -12x - 11 Ask: how many x’s in -12x?-12 Multiply -12 by x + 2 and subtract -12x -24 13 Remainder is 13 Quotient: Change signs when subtracting! Insert a place-holding 0x

8. Homework pg. 687 #15-21 odd #27-45 odd