1. 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

2. 6.3a Dividing Polynomials by Jason L. Bradbury CA State Standard - 3.0 Students are adept at operations on polynomials, including long division. Objective – To be able divide polynomials by long division and synthetic division.

3. 3 Long Division: 2 2 7 5 2 1 1 7 7 1 5 2 5 2 4 1 6.3a Dividing Polynomials Example 1: Divide 2275 by 3 58 758 + 1 3 758, 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. 4 Long Division: 3 7 1 1 3 6 1 1 9 8 3 1 2 8 3 Example 2: Divide 3711 by 4 27 9 2 7 + 3 4

5. 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 + 7 + 5 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

6. x + 2 Polynomial Long Division: x 2 + 10x + 16 x2x2x2x2 8x + 16 0 Example 4: Divide x 2 + 10x + 16 by x + 2 x+ 8 + 2x x + 8

7. 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 + 2 3 Example 4: Divide x 4 + 2x 2 –x + 5 by x 2 – x + 1 + x+ 2 – x 3 + x 2 x 2 + x + 2 + 3 x 2 – x + 1

8. 6.3a Homework Page 330 – 331 1 – 7 odd