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.

Simple example.

We will divide the polynomial 4x^{3} + 10x^{2} + 4x by the monomial 2x:

(4x^{3} + 10x^{2} + 4x)/2x

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

2x(2x^{2} + 5x + 2)/2x

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

2x(2x^{2} + 5x + 2)/2x = 2x^{2} + 5x + 2

So the answer is:

(4x^{3} + 10x^{2} + 4x)/2x = 2x^{2} + 5x + 2

Next example.

We will divide the polynomial 5a^{2}b^{4} + 15a^{2}b^{3} by the monomial 5ab:

(5a^{2}b^{4} + 15a^{2}b^{3})/5ab

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

5ab(ab^{3} + 3ab^{2})/5ab

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

5ab(ab^{3} + 3ab^{2})/5ab = ab^{3} + 3ab^{2}

So the answer is:

(5a^{2}b^{4} + 15a^{2}b^{3})/5ab = ab^{3} + 3ab^{2}