# What is long division of polynomials?

May 8, 2018

#### Explanation:

Given: What is long division of polynomials?

Long division of polynomials is very similar to regular long division. It can be used to simplify a rational function $\frac{N \left(x\right)}{D \left(x\right)}$ for integration in Calculus, to find a slant asymptote in PreCalculus, and many other applications. It is done when the denominator polynomial function has a lower degree than the numerator polynomial function. The denominator can be a quadratic.

Ex. $y = \frac{{x}^{2} + 12}{x - 2}$

" "ul(" "x + 2" ")
$x - 2 | {x}^{2} + 0 x + 12$
$\text{ } \underline{{x}^{2} - 2 x}$
$\text{ } 2 x + 12$
" "ul(2x -4" ")
$\text{ } 16$

This means $y = \frac{{x}^{2} + 12}{x - 2} = x + 2 + \frac{16}{x - 2}$

The slant asymptote in the above example is $y = x + 2$