Transcript Slide 1

Dividing Polynomials
MATH 018
Combined Algebra
S. Rook
Overview
• Section 5.7 in the textbook:
– Dividing by monomials
– Dividing by polynomials
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Dividing by Monomials
Dividing by Monomials
• Recall that a monomial is a polynomial
with ONE term
• When a denominator contains a
monomial:
– Divide the monomial into each term of the
numerator
– Simplify using exponent rules
– Remember to leave NO negative exponents
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Dividing by Monomials
(Example)
Ex 1: Simplify – leave NO negative
exponents:
4
5
9
x

6
x
 2x
a)
4x2
2
4
2
x

6
xy
 12xy
b)
6x2 y
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Dividing by Polynomials
Dividing by Polynomials
• When the denominator or divisor is something
other than a monomial
– Must use process of long division
• Recall that when subtracting polynomials,
distribute the negative through the second
polynomial
– i.e. Change to addition by swapping the signs of the
second polynomial
• Stop after the subtraction that results when the
last term of the dividend (polynomial inside the
division) has been brought down
– The result is the remainder
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Dividing Polynomials (Example)
Ex 2: Simplify:
x 2  2 x  48
a)
x6
2
15
x
 17x  4
b)
3x  4
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Dividing Polynomials (Example)
Ex 3: Simplify:
4 x3  6 x 2  2 x  9
a)
x2
9 x 2  2 x  11
b)
x5
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Missing Terms in the Dividend
• When the dividend contains missing
term(s):
– Rewrite the dividend with zeros for the
missing term(s)
• These zeros serve as placeholders
• Possible to have the missing term(s) appear in the
multiplication step
– Proceed as normal
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Dividing Polynomials (Example)
Ex 4: Simplify:
x3  8x  3
a)
x4
3x 3  2 x 2  10
b)
x 1
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Summary
• After studying these slides, you should
know how to do the following:
– Divide by a monomial
– Divide by a polynomial
• Additional Practice
– See the list of suggested problems for 5.7
• Next lesson
– GCF & Factor by Grouping (Section 6.1)
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