joyce duvall green valley high school henderson, nv
TRANSCRIPT
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Joyce DuVallGreen Valley High School
Henderson, NV
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Dividing Polynomials
The objective is to be able to divide a polynomial by a monomial.
( )6 3 32x x
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Step 1
( )6 3 32x x Divide each term of the polynomial by the monomial.
6
3
3
3
2x
x x
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Step 2
6
3
3
3
2x
x x
Factor each expression.
2 3
3
3
3
x x
x x
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Step 32 3
3
3
3
x x
x xDivide out the common factors in each expression.
2 3
3
3
3
x x
x x
The numbers and variables which are crossed out divide out to 1.
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Step 4
2 3
3
3
3
x x
x xWrite in simplified form.
21
xx
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1 . 8 x 3 3 2 4x x A
2 . ( )1 2 2 3 22x x x A
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Dividing a Polynomial by a Polynomial
The objective is to be able to divide a polynomial by a polynomial by using long division.
Dividend – the number which is being divided.
Divisor – The number that is being divided into the dividend.
Quotient – The result obtained when numbers or expressions are divided.
Remainder – The part that is left over when the divisor no longer goes into the dividend a whole number of times.
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Polynomial Long Division
D iv id e b y x x x2 3 1 2 .
Step 1: Write it as you would a regular long division problem.
x x x 2 3 12
The x+2 is the divisor and the x2+3x-1 is the dividend.
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Step 2
x x x 2 3 12
x
x x
x
2
1
1x x x 2 32
2
Divide x2 by x to get x. Place this on top.
Multiply x+2 by x to get x2 +2x.Subtract the x2+2x from the x2+3x-1.
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Step 3
Divide the x by x to get 1.
Multiply x+2 by 1 to get x+2.
Subtract x+2 from the x-1.
x
2
3
1
3
2
2
2
x x xx
x x
x
2 1
1
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Step 4
Write your final answer.
x x x
xx
2 3 1 2
13
2
d iv id ed b y is
The x+1 is the quotient.
T h e -3
x + 2 is th e rem ain d er.
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1 . x - 2x x2 1 5
2 . 1 2 5 1 0 4 12x x x
A
A