Dividing Polynomials Topic Index | Algebra Index | Regents Exam Prep Center
 We will be examining polynomials divided by monomials and by binomials.

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
 Keep this in mind

* 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: The polynomial on the top has 3 terms and the answer has 3 terms. Notice how the numbers (the coefficients) were divided. Answer: Notice how the exponents were subtracted. Notice how the last term reduced to one.

 Think about it: Dividing by a number is the same process as multiplying by the reciprocal of that number. Notice how we used the reciprocal of 4x2 Answer: Now the reciprocal was distributed across the parentheses and the problem proceeds as in the example above.

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.

Examples:  (see more under "Factoring" section)

 1. Notice that the x+1 was reduced as a "set". 2.
 3. 4. Tricky strategy:  Notice that the -1 was factored out of the numerator to create a binomial compatible with the one in the denominator. 2 - x = -1(x - 2)

 If you are solving multiple choice questions, you can use the calculator to "check" your work with polynomials. You can use a Numerical Checking process:  Numerical Process                                   or You can use an Equation Checking process::  Equation Process

 Topic Index | Algebra Index | Regents Exam Prep Center Created by Lisa Schultzkie