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: (factorable situations only)

 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.