1.3 Dividing polynomials

If the polynomials have $({\hbox{degree}}\,f)\geq({\hbox{degree}}\,g)$, then we can use polynomial long division to write

where $q(x)$ is a polynomial and $r(x)$ is a polynomial with $({\hbox{degree}}\,r)<({\hbox{degree}}\,g)$. (See MATH111, Thm. 7.1.10 for a proof.) It is easy to integrate the polynomial $q(x).$