6.6 Divide polynomials

Divide a polynomial by a monomial

In the last section, you learned how to divide a monomial by a monomial. As you continue to build up your knowledge of polynomials the next procedure is to divide a polynomial of two or more terms by a monomial    .

The method we’ll use to divide a polynomial by a monomial is based on the properties of fraction addition. So we’ll start with an example to review fraction addition.

$\begin{array}{cccc}\text{The sum,}\hfill & & & \frac{y}{5}+\frac{2}{5},\hfill \\ \text{simplifies to}\hfill & & & \frac{y+2}{5}.\hfill \end{array}$

Now we will do this in reverse to split a single fraction into separate fractions.

We’ll state the fraction addition property here just as you learned it and in reverse.

We use the form on the left to add fractions and we use the form on the right to divide a polynomial by a monomial.

$\begin{array}{cccc}\text{For example,}\hfill & & & \frac{y+2}{5}\hfill \\ \text{can be written}\hfill & & & \frac{y}{5}+\frac{2}{5}.\hfill \end{array}$

We use this form of fraction addition to divide polynomials by monomials.

Remember that division can be represented as a fraction. When you are asked to divide a polynomial by a monomial and it is not already in fraction form, write a fraction with the polynomial in the numerator and the monomial in the denominator.

When we divide by a negative, we must be extra careful with the signs.