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UNIT 2, LESSON 3
POLYNOMIAL DIVISION
Adapted by Mrs. King from www.meidistance.co.uk/pdf/Dividing%20polynomials.ppt
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BLAST FROM THE PAST…
8327565
![Page 3: UNIT 2, LESSON 3 POLYNOMIAL DIVISION Adapted by Mrs. King from 20polynomials.ppt](https://reader035.vdocument.in/reader035/viewer/2022081515/5697bfd51a28abf838cad58c/html5/thumbnails/3.jpg)
BLAST FROM THE PAST…
8327565
How many times does 5 go into 8?
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BLAST FROM THE PAST…
8327565
How many times does 5 go into 8?
1
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BLAST FROM THE PAST…
8327565
How many times does 5 go into 8?
1
5
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BLAST FROM THE PAST…
8327565
How many times does 5 go into 8?
Subtract
1
53
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BLAST FROM THE PAST…
8327565
How many times does 5 go into 8?
Subtract
Bring down
1
533
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ALGEBRAIC LONG DIVISION
Divide (2x³ + 3x² - x + 1) by (x + 2)
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ALGEBRAIC LONG DIVISION
Divide (2x³ + 3x² - x + 1) by (x + 2)
3 22 2 3 1x x x x x + 2 is the divisor
The quotient will be here.
2x³ + 3x² - x + 1 is the dividend
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ALGEBRAIC LONG DIVISION
First divide the first term of the dividend, 2x³, by x (the first term of the divisor).
3 22 2 3 1x x x x
22xThis gives 2x². This will be the first term of the quotient.
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ALGEBRAIC LONG DIVISION
Now multiply 2x² by x + 2
3 22 2 3 1x x x x 3 22 4x x
22x
2xand subtract
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ALGEBRAIC LONG DIVISION
Bring down the next term, -x.
3 22 2 3 1x x x x 3 22 4x x
22x
2x x
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ALGEBRAIC LONG DIVISION
Now divide –x², the first term of –x² - x, by x, the first term of the divisor
3 22 2 3 1x x x x 3 22 4x x
22x
2x x
x
which gives –x.
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ALGEBRAIC LONG DIVISION
Multiply –x by x + 2
3 22 2 3 1x x x x 3 22 4x x
22x
2x x
x
2 2x x
xand subtract
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ALGEBRAIC LONG DIVISION
Bring down the next term, 1 x
3 22 2 3 1x x x x 3 22 4x x
22x
2x x
x
2 2x x
1
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ALGEBRAIC LONG DIVISION
Divide x, the first term of x + 1, by x, the first term of the divisor
13 22 2 3 1x x x x 3 22 4x x
22x
2x x
x
2 2x x
x 1which gives 1
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ALGEBRAIC LONG DIVISION
Multiply x + 2 by 1
3 22 2 3 1x x x x 3 22 4x x
22x
2x x
x
2 2x x
x
1
12x 1and subtract
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ALGEBRAIC LONG DIVISION
The remainder is –1.
3 22 2 3 1x x x x 3 22 4x x
22x
2x x
x
2 2x x
x
1
12x 1
The quotient is 2x² - x + 1
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Divide 125x3 - 8 by 5x - 2
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Divide 125x3 - 8 by 5x - 2
80012525 23 xxxx
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Divide 125x3 - 8 by 5x - 2
80012525 23 xxxx
225x
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Divide 125x3 - 8 by 5x - 2
80012525 23 xxxx
225x
23 50125 xx
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Divide 125x3 - 8 by 5x - 2
80012525 23 xxxx
225x
23 50125 xx 250x
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Divide 125x3 - 8 by 5x - 2
80012525 23 xxxx
225x
23 50125 xx xx 050 2
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Divide 125x3 - 8 by 5x - 2
80012525 23 xxxx
225x
23 50125 xx xx 050 2
x10
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Divide 125x3 - 8 by 5x - 2
80012525 23 xxxx
225x
23 50125 xx xx 050 2
x10
xx 2050 2
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Divide 125x3 - 8 by 5x - 2
80012525 23 xxxx
225x
23 50125 xx xx 050 2
x10
xx 2050 2 820 x
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Divide 125x3 - 8 by 5x - 2
80012525 23 xxxx
225x
23 50125 xx xx 050 2
x10
xx 2050 2 820 x
4
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Divide 125x3 - 8 by 5x - 2
80012525 23 xxxx
225x
23 50125 xx xx 050 2
x10
xx 2050 2 820 x
4
820 x
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Divide 125x3 - 8 by 5x - 2
80012525 23 xxxx
225x
23 50125 xx xx 050 2
x10
xx 2050 2 820 x
4
820 x0
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SYNTHETIC DIVISION
• When the divisor (what we're dividing by) is of the form x-a, we can use synthetic division instead of long division to find the quotient and remainder.
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SYNTHETIC DIVISION
• Divide by
612583 2345 xxxxx 2x
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SYNTHETIC DIVISION
6125832
Place the opposite of the divisor to the left of the coefficients of the
dividend
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SYNTHETIC DIVISION
3
6125832
Carry down the first coefficient
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SYNTHETIC DIVISION
3
6
6125832
Multiply by the
divisor
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SYNTHETIC DIVISION
23
6
6125832
ADD!
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SYNTHETIC DIVISION
874123
148246
6125832
Continue to multiply by the divisor and ADD until you reach the end.
*Box off the last answer! This is your remainder!
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SYNTHETIC DIVISION
874123
148246
6125832
Continue to multiply by the divisor and ADD until you reach the end.
*Box off the last answer! This is your remainder!
These are the coefficients of your answer!
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SYNTHETIC DIVISION
874123
148246
6125832
To find the polynomial form of the quotient, start with an exponent one-degree smaller than the original dividend
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SYNTHETIC DIVISION
874123
148246
6125832
To find the polynomial form of the quotient, start with an exponent one-degree smaller than the original dividend
87423 234 Rxxxx