
Dividing a Polynomial by a Monomial:

When dividing a polynomial by a monomial,
divide EACH term of the polynomial by the monomial.
Remember to use the quotient rule for exponents.


When dividing a polynomial by a monomial, the number of terms in the polynomial equals the number of terms in the answer. 


When dividing by a monomial, numbers (or expressions)
do not "cancel" and disappear!
A number (or expression) divided by itself equals one. 

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



Dividing a Polynomial by a Binomial: (also check out Factoring)

When dividing a polynomial by a binomial, FACTOR completely both the numerator and denominator (the dividend and divisor) before reducing. Reduce the greatest common factors from the numerator and denominator. 

The terms in a binomial cannot be separated from one another when reducing. For example, in the binomial 4x  1, the 4x cannot be reduced by itself. You must reduce the entire expression 4x  1. 


Factor the numerator.
Reduce the common factor of x + 3.



Factor the numerator.
Reduce the common factor of a  5.



Factor the numerator.
Reduce the common factor
y + 2.



Factor the numerator.
Factor the denominator.
Reduce the common factor of x + 2.

Sneaky one!!


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. 
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