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
Page 330 – 331 Page 330 – 331
1 – 7 odd1 – 7 odd
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