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I have added to the original presentation in response to one of the comments.... the result of 'x' is correct on slide 7, take a look at the new version of this ppt to clear up any confusion about why...
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Dividing polynomials
This PowerPoint presentation demonstrates two different methods
of polynomial division.
© Kristen A. Treglia 2007
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 divisionMultiply –x by x + 2
3 22 2 3 1x x x x 3 22 4x x
22x
2x x
x
2 2x x To get a result of:
Algebraic long division
Now subtract
3 22 2 3 1x x x x 3 22 4x x
22x
2x x
x
2 2x x
** remember, you must subtract both the –x2 term and the -2x term
Algebraic long division
Now combine like terms
3 22 2 3 1x x x x 3 22 4x x
22x
2x x
x
2 2x x
x
(since we subtracted two negative terms they both turned into positive terms)
{
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