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**Ch 11.5 Dividing Polynomials**

Objective: To divide polynomials using long division.

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**Definitions Rules dividend ÷ divisor = quotient**

Multiply the first term of the divisor by a value that will eliminate the first term of the dividend Distribute that value to the divisor and subtract it from the dividend 3) Repeat 1 & 2 until there is a remainder

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**a x Example 1 Example 2 -4 +3 − ( ) a2 − 7a − ( ) x2 + 5x -4a + 36 3x**

(a2 – 11a + 36) ÷ (a – 7) (x2 + 8x + 18) ÷ (x + 5) a -4 x +3 − ( ) a2 − 7a − ( ) x2 + 5x -4a + 36 3x + 18 − ( ) -4a + 28 − ( ) 3x + 15 8 3 a – x a - 7 x + 5

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**v 5n Example 3 Example 4 -7 +7 − ( ) v2 + 8v − ( ) 5n2 − 30n -7v − 57**

(v2 + v − 57) ÷ (v + 8) (5n2 − 23n − 33) ÷ (n − 6) v -7 5n +7 − ( ) v2 + 8v − ( ) 5n2 − 30n -7v − 57 7n − 33 − ( ) -7v − 56 − ( ) 7n − 42 -1 9 v – 5n v + 8 n − 6

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**1) 2) 3) 4) r + 8 + 5 n – 8 + 8 r + 7 n + 5 x + 9 + -3 m + 10 + -9**

Classwork 1) 2) (r2 + 15r + 61) ÷ (r + 7) (n2 – 3n – 32) ÷ (n + 5) r n – r + 7 n + 5 3) 4) (m2 + 12m + 11) ÷ (m + 2) (x2 – x – 93) ÷ (x – 10) x m x − 10 m + 2

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**5) 6) 7) 8) x + 3 + 3 n + 8 + -3 x + 5 n + 3 x + 4 + -3 8m – 9 + -3**

(x2 + 8x + 18) ÷ (x + 5) (n2 + 11n + 21) ÷ (n + 3) x n x + 5 n + 3 7) 8) (x2 + x – 15) ÷ (x – 3) (8m2 + 39m – 57) ÷ (m + 6) x 8m – x − 3 m + 6

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