Warm - up 6.3a Simplify: 1. 4x 3 2. 5x 2 4x x 2 x 2 5 x + 7 Find the missing factor: 3. x 2 – 2x – 63 = (x-9)(?) 4. 2x 2 + 13x + 15 = (x+5)(?) 2x + 3.

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Presentation transcript:

Warm - up 6.3a Simplify: 1. 4x x 2 4x x 2 x 2 5 x + 7 Find the missing factor: 3. x 2 – 2x – 63 = (x-9)(?) 4. 2x x + 15 = (x+5)(?) 2x + 3

6.3a Dividing Polynomials by Jason L. Bradbury CA State Standard Students are adept at operations on polynomials, including long division. Objective – To be able divide polynomials by long division and synthetic division.

3 Long Division: a Dividing Polynomials Example 1: Divide 2275 by , R 1 22 divided by 3 is 7 SUBTRACT Multiply 7 times 3 17 divided by 3 is 5 Multiply 5 times 3 SUBTRACT 25 divided by 3 is 8 Multiply 8 times 3 SUBTRACT Remainder is 1 out of 3 Summary:

4 Long Division: Example 2: Divide 3711 by

x – 5 Polynomial Long Division: x 2 + 2x – 30 x2x2x2x2 7x – 30 7x – 35 5 Example 3: Divide x 2 + 2x – 30 by x – 5 x+ 7 – 5x x x – 5 Multiply x times (x – 5) *SUBTRACT: change signs Multiply 7 times (x – 5) *SUBTRACT: change signs Remainder 5 out of x - 5 Divide

x + 2 Polynomial Long Division: x x + 16 x2x2x2x2 8x Example 4: Divide x x + 16 by x + 2 x x x + 8

x 2 – x + 1 Polynomial Long Division: x 4 + 0x 3 + 2x 2 – x + 5 x4x4x4x4 x 3 + x 2 – x x2x2 x 3 – x 2 + x 2x 2 – 2x + 5 2x 2 – 2x Example 4: Divide x 4 + 2x 2 –x + 5 by x 2 – x x+ 2 – x 3 + x 2 x 2 + x x 2 – x + 1

6.3a Homework Page 330 – – 7 odd