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Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 6.5 - 1
Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 6.5 - 2
Exponents, Polynomials, and
Polynomial Functions
Chapter 6
Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 6.5 - 3
6.5
Dividing Polynomials
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.5 - 4
6.5 Dividing Polynomials
Objectives
1. Divide a polynomial by a monomial.
2. Divide a polynomial by a polynomial of two or more terms.
3. Divide polynomial functions.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.5 - 5
6.5 Dividing Polynomials
Dividing a Polynomial by a Monomial
We can check this answer by multiplying the quotient by the divisor to obtain the original polynomial.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.5 - 6
6.5 Dividing Polynomials
Dividing a Polynomial by a Monomial
Why is the answer not a polynomial?All variables must have whole number exponents and no variables can be in the denominator or under radicals.
y is in the denominator
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.5 - 7
6.5 Dividing Polynomials
Dividing a Polynomial by a Polynomial
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6.5 Dividing Polynomials
Dividing a Polynomial by a Polynomial
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.5 - 9
6.5 Dividing Polynomials
Dividing a Polynomial by a Polynomial
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.5 - 10
6.5 Dividing Polynomials
Dividing a Polynomial with a Missing Term
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.5 - 11
6.5 Dividing Polynomials
Dividing a Polynomial with a Missing Term
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.5 - 12
6.5 Dividing Polynomials
Dividing a Polynomial with a Missing Term
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.5 - 13
6.5 Dividing Polynomials
Dividing a Polynomial with a Missing Term
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.5 - 14
6.5 Dividing Polynomials
Dividing a Polynomial with a Missing Term
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.5 - 15
6.5 Dividing Polynomials
Dividing a Polynomial with a Missing Term
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.5 - 16
6.5 Dividing Polynomials
Dividing a Polynomial with a Missing Term
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.5 - 17
6.5 Dividing Polynomials
Dividing Polynomial Functions
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.5 - 18
6.5 Dividing Polynomials
Dividing Polynomial Functions
Applying the definition of dividing functions:
Performing division as shown earlier
Results are the same