###### Example6.5.3

Simplify $$\dfrac{2x^3+4x^2-10x}{2}\text{.}$$

The first step will be to recognize that the $$2$$ we're dividing by will be divided into every term of the numerator. Once we recognize that, we will simply perform that division.

\begin{align*} \frac{2x^3+4x^2-10x}{2}\amp=\frac{2x^3}{2}+\frac{4x^2}{2}+\frac{-10x}{2}\\ \amp=x^3+2x^2-5x \end{align*}

Once you become comfortable with this process, you will often leave out the step where we wrote out the distribution. You will do the distribution in your head and this will often become a one-step problem.

in-context