# How do you simplify (5x^4-13x^3+21x^2+x+10)/(5x-3)?

Feb 1, 2017

Try long division instead of synthetic division.

${x}^{3} - 2 {x}^{2} + 3 x + 2 + \frac{16}{5 x - 3}$

#### Explanation:

I decided to do this one on paper so that it is easier to explain.

Long division is just like regular long division except that there are variables and numbers.

Here the 16 remainder at the end means that the last term is $\frac{16}{5 x - 3}$ because it was divided by 5x-3 but could not get divided out like the other terms. Often, the remainder is zero for these types of questions.

Thus the final equation would be ${x}^{3} - 2 {x}^{2} + 3 x + 2 + \frac{16}{5 x - 3}$

For more information on polynomial long division, check out this site: