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#