Question

What is long division of polynomials?

Answer 1

See answer below

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 `(N(x))/(D(x))` 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 = (x^2 + 12)/(x - 2)`

`" "ul(" "x + 2" ")`
`x - 2|x^2 + 0x + 12`
`" "ul(x^2 -2x)`
`" "2x + 12`
`" "ul(2x -4" ")`
`" "16`

This means `y = (x^2 + 12)/(x - 2) = x + 2 + 16/(x-2)`

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