unit 2, lesson 3 polynomial division adapted by mrs. king from 20polynomials.ppt
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UNIT 2, LESSON 3
POLYNOMIAL DIVISION
Adapted by Mrs. King from www.meidistance.co.uk/pdf/Dividing%20polynomials.ppt
BLAST FROM THE PAST…
8327565
BLAST FROM THE PAST…
8327565
How many times does 5 go into 8?
BLAST FROM THE PAST…
8327565
How many times does 5 go into 8?
1
BLAST FROM THE PAST…
8327565
How many times does 5 go into 8?
1
5
BLAST FROM THE PAST…
8327565
How many times does 5 go into 8?
Subtract
1
53
BLAST FROM THE PAST…
8327565
How many times does 5 go into 8?
Subtract
Bring down
1
533
ALGEBRAIC LONG DIVISION
Divide (2x³ + 3x² - x + 1) by (x + 2)
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
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.
ALGEBRAIC LONG DIVISION
Now multiply 2x² by x + 2
3 22 2 3 1x x x x 3 22 4x x
22x
2xand subtract
ALGEBRAIC LONG DIVISION
Bring down the next term, -x.
3 22 2 3 1x x x x 3 22 4x x
22x
2x x
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.
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
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
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
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
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
Divide 125x3 - 8 by 5x - 2
Divide 125x3 - 8 by 5x - 2
80012525 23 xxxx
Divide 125x3 - 8 by 5x - 2
80012525 23 xxxx
225x
Divide 125x3 - 8 by 5x - 2
80012525 23 xxxx
225x
23 50125 xx
Divide 125x3 - 8 by 5x - 2
80012525 23 xxxx
225x
23 50125 xx 250x
Divide 125x3 - 8 by 5x - 2
80012525 23 xxxx
225x
23 50125 xx xx 050 2
Divide 125x3 - 8 by 5x - 2
80012525 23 xxxx
225x
23 50125 xx xx 050 2
x10
Divide 125x3 - 8 by 5x - 2
80012525 23 xxxx
225x
23 50125 xx xx 050 2
x10
xx 2050 2
Divide 125x3 - 8 by 5x - 2
80012525 23 xxxx
225x
23 50125 xx xx 050 2
x10
xx 2050 2 820 x
Divide 125x3 - 8 by 5x - 2
80012525 23 xxxx
225x
23 50125 xx xx 050 2
x10
xx 2050 2 820 x
4
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
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
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.
SYNTHETIC DIVISION
• Divide by
612583 2345 xxxxx 2x
SYNTHETIC DIVISION
6125832
Place the opposite of the divisor to the left of the coefficients of the
dividend
SYNTHETIC DIVISION
3
6125832
Carry down the first coefficient
SYNTHETIC DIVISION
3
6
6125832
Multiply by the
divisor
SYNTHETIC DIVISION
23
6
6125832
ADD!
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!
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!
SYNTHETIC DIVISION
874123
148246
6125832
To find the polynomial form of the quotient, start with an exponent one-degree smaller than the original dividend
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
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