Warm - up 6.3aWarm - up 6.3aSimplify:

1. 4x3 2. 5x2

4x

x2 x2

5

x + 7

Find the missing factor:3. x2 – 2x – 63 = (x-9)(?)

4. 2x2 + 13x + 15 = (x+5)(?) 2x + 3

6.3a Dividing 6.3a Dividing PolynomialsPolynomials

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

Long Division:

2 2 7 52 2 7 52 12 1

1 71 7

7

1 51 5

2 52 52 4 2 4

1

6.3a Dividing Polynomials6.3a Dividing Polynomials

Example 1:

Divide 2275 by 3

5 8

758 + 1

3

758, R 1

22 divided by 3 is 7

SUBTRACT

Multiply 7 times 3

17 divided by 3 is 5Multiply 5 times 3

SUBTRACT

25 divided by 3 is 8

Multiply 8 times 3SUBTRACTRemainder is 1 out of 3

Summary:

4

Long Division:Long Division:

3 7 1 13 7 1 13 63 6

1 11 1

9

88

3 13 12 8 2 8

3

Example 2:

Divide 3711 by 4

2 7

9 2 7 + 3

4

x – 5

Polynomial Long Division:Polynomial Long Division:

xx22 + 2x – 30 + 2x – 30 xx22

7x – 30 7x – 30 7x7x – 35– 35

5

Example 3:Example 3:

Divide x2 + 2x – 30 by x – 5

x + 7

– – 5x5x

x + 7 + 5

x – 5

2xx

x

Multiply x times (x – 5)

*SUBTRACT: change signs

77

x

x

Multiply 7 times (x – 5)

*SUBTRACT: change signs

Remainder 5 out of x - 5

Divide

Divide

x + 2

Polynomial Long Division:Polynomial Long Division:

xx22 + 10x + 16 + 10x + 16 xx22

8x + 16 8x + 16 8x8x + 16+ 16

0

Example 4:Example 4:

Divide x2 + 10x + 16 by x + 2

x + 8

+ 2x+ 2x

x + 8

x2 – x + 1

Polynomial Long Division:Polynomial Long Division:

xx44 + + 0x0x33 + 2x + 2x22 – x + 5 – x + 5xx44

xx33 + x + x22 – x – x

x2

xx3 3 – x– x22 + x + x

2x2x22 – 2x + 5 – 2x + 52x2x2 2 – 2x + 2 – 2x + 2

33

Example 4:Example 4:

Divide x4 + 2x2 –x + 5 by x2 – x + 1

+ x + 2

– – xx33 + x+ x22

x2 + x + 2 + 3

x2 – x + 1

6.3a Homework6.3a Homework

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1 – 7 odd1 – 7 odd