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## Dividing Polynomials

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**Dividing Polynomials**Using Long Division**Terminology**Dividend – Numerator Divisor – Denominator Quotient Remainder**Steps to Divide**• Divide • Multiply • Subtract • Bring Down • Shampoo, Rinse, Repeat (if necessary)**Quick Remembrance**5 1 1 Set up to divide. • Divide 7 by 5. • Multiply 1 by 5. • Subtract down (7–5) • Bring Down 5. • Divide 25 by 5. • Multiply 5 by 5. • Subtract Down (25–25) • Bring Down 5. • Divide 05 by 5. • Multiply 1 by 5. • Subtract Down (5–5) 5 5 25 5 5 Remainder**x**+1 • Divide x2 by x, which is x. • Multiply x by x + 3, which is x2 + 3x. • Subtract (x2 + 4x) - (x2 + 3x), which is x. • Bring down the 3. • Repeat using x + 3 as our new divisor. 0 Divide x by x, which is 1. Multiply 1 by x + 3, which is x+ 3. Subtract (x + 3) - (x+ 3), which is 0 (remainder).**x**+2 • Divide x2 by x, which is x. • Multiply x by x + 1, which is x2 + x. • Subtract (x2 + 3x) – (x2 + x), which is 2x. • Bring down the -6. • Repeat using 2x – 6 as our new divisor. -8 Divide x by x, which is 2. Multiply 2 by x + 1, which is 2x+ 2. Subtract (2x – 6) – (2x+ 2), which is -8 (remainder).**Divide**Multiply Subtract Bring Down Repeat (if necessary)**Divide**Multiply Subtract Bring Down Repeat (if necessary) Remainder**Divide**Multiply Subtract Bring Down Repeat (if necessary) Remainder**Divide**Multiply Subtract Bring Down Repeat (if necessary)**Divide**Multiply Subtract Bring Down Repeat (if necessary)