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How to divide polynomials by a monomial

Dividing polynomials by a monomial is simple. The following example will help you to divide polynomials by a monomial. We will explain how to divide a polynomial by a monomial step by step.

Dividing a polynomial by a monomial

Simple example.

We will divide the polynomial 4x3 + 10x2 + 4x by the monomial 2x:

(4x3 + 10x2 + 4x)/2x

Here we can factor out the common factor 2x from the numerator:

2x(2x2 + 5x + 2)/2x

Cancel the common factor 2x off and get the result:

2x(2x2 + 5x + 2)/2x = 2x2 + 5x + 2

So the answer is:

(4x3 + 10x2 + 4x)/2x = 2x2 + 5x + 2
Next example.

We will divide the polynomial 5a2b4 + 15a2b3 by the monomial 5ab:

(5a2b4 + 15a2b3)/5ab

Here we can factor out the common factor 5ab from the numerator:

5ab(ab3 + 3ab2)/5ab

Cancel the common factor 5ab off and get the result:

5ab(ab3 + 3ab2)/5ab = ab3 + 3ab2

So the answer is:

(5a2b4 + 15a2b3)/5ab = ab3 + 3ab2