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Section 1.9

Division of Algebraic Expressions

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I. Dividing Monomials

• Divide the numerical coefficients; then divide the literal numbers (variables) using the properties of exponents.

3 2

2 3

52

4

x yz

x yz

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II. Dividing Multinomial by Monomial

• Divide each term of the numerator (multinomial) by monomial separately, and then simplify each fraction. a b c a b c

d d d d

2 3 2

2

9 3 4

2

x y xy y

x y

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III. Dividing Polynomial by Polynomial (Algebraic Long Division)

First we will revisit the long division algorithm for arithmetic

12 46,313

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Algebraic Long Division

• Before you get started with the algebraic division algorithm,

– Write the divisor and the dividend in descending order

– Use zero place holders for any “missing” terms

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Long Division Example #1

25 2 7 1x x x

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Long Division Example #23 27

3

x

x

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Long Division Example #32 37 5 8 6

2 1

x x x

x