Dividing Polynomials
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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.

Remember that numbers do not cancel and disappear!  A number divided by itself is 1.  It reduces to the number 1.

Remember to write the appropriate sign in between the terms.


The polynomial on the top has 3 terms and the answer has 3 terms.

Notice how the numbers (the coefficients) were divided. 


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  


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.

Factor completely both the numerator and denominator before reducing.

Divide both the numerator and denominator by their greatest common factor.

Examples:  (see more under "Factoring" section)



Notice that the x+1 was reduced as a "set".






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
You can use an Equation Checking process: Equation Process