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1. Warm - up 6.3a Simplify: 1. 4x3 2. 5x2 x2 x2 4x 5 Find the missing factor: 3. x2 – 2x – 63 = (x-9)(?) x + 7 4. 2x2 + 13x + 15 = (x+5)(?) 2x + 3

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

3. 3 Long Division: 6.3a Dividing Polynomials 1 758 + 3 Example 1: Divide 2275 by 3 Summary: 7 5 8 22 divided by 3 is 7 2 2 7 5 Multiply 7 times 3 2 1 SUBTRACT 17 divided by 3 is 5 758,R 1 1 7 Multiply 5 times 3 1 5 SUBTRACT 25 divided by 3 is 8 2 5 Multiply 8 times 3 2 4 SUBTRACT Remainder is 1 out of 3 1

4. 4 Long Division: 3 9 2 7 + 4 Example 2: Divide 3711 by 4 9 2 7 3 7 1 1 3 6 1 1 8 3 1 2 8 3

5. x – 5 Polynomial Long Division: 5 x + 7 + x – 5 Example 3: Divide x2 + 2x – 30 by x – 5 x + 7 Divide x2 + 2x – 30 Multiply x times (x – 5) x2 – 5x *SUBTRACT: change signs 7x – 30 Divide 7x– 35 Multiply 7 times (x – 5) 5 *SUBTRACT: change signs Remainder 5 out of x - 5

6. x + 2 Polynomial Long Division: Example 4: Divide x2 + 10x + 16 by x + 2 x + 8 x2 + 10x + 16 x2 + 2x 8x + 16 8x+ 16 0 x + 8

7. x2 – x + 1 Polynomial Long Division: 3 x2 + x + 2 + x2 – x + 1 Example 4: Divide x4 + 2x2 –x + 5 by x2 – x + 1 x2 + x + 2 x4 + 0x3 + 2x2 – x + 5 x4 – x3 + x2 x3 + x2 – x x3 – x2 + x 2x2 – 2x + 5 2x2 – 2x + 2 3

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