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Dividing Polynomials

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Dividing Polynomials

We will be examining polynomials divided by monomials and by binomials.

Dividing a Polynomial by a Monomial:

Steps for Dividing a Polynomial by a Monomial:

  1. Divide each term of the polynomial by the monomial.
    a) Divide numbers (coefficients)
    b) Subtract exponents
    Dividing Polynomials 1
    * The number of terms in the polynomial equals the number of terms in the answer when dividing by a monomial.
  2. Remember that numbers do not cancel and disappear! A number divided by itself is 1. It reduces to the number 1.
  3. Remember to write the appropriate sign in between the terms.

Example 1:
Dividing Polynomials 2

Another way of looking at “dividing by a monomial” is multiplying by the reciprocal of the monomial. See Example 2.

Example 2:

Dividing Polynomials 3

Dividing a Polynomial by a Binomial:

Steps for Dividing a Polynomial by a Binomial:

  1. Remember that the terms in a binomial cannot be separated from one another when reducing. For example, in the binomial 2x + 3, the 2x can never be reduced unless the entire expression 2x + 3 is reduced.
  2. Factor completely both the numerator and denominator before reducing.
  3. Divide both the numerator and denominator by their greatest common factor.

Example 1:
Factor the numerator.
Reduce the common factor of x + 3.
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Example 2:
Factor the numerator.
Reduce the common factor of a – 5.
Dividing Polynomials 5

Example 3:
Factor the numerator.
Reduce the common factor y + 2.
Dividing Polynomials 6

Example 4:
Factor the numerator.
Factor the denominator.
Reduce the common factor of x + 2.
Dividing Polynomials 7

Example 5:
7 – x and x – 7 are “almost” the same, except that the signs of the terms are opposite one another. To create a situation that will allow for reducing, factor out -1 from one of these binomials.
Dividing Polynomials 8

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