# polynomial f(x)

• Feb 13th 2008, 06:03 AM
ihmth
polynomial f(x)
Need help pls

a.) Show that for any polynomial f(x) there exists a polynomial g(x) such that
f(x) = x*g(x) + c, where c is a constant.

b.) Use the result in letter a.) and the remainder theorem to prove the factor theorem.

--tnx
• Feb 13th 2008, 06:13 AM
ThePerfectHacker
Quote:

Originally Posted by ihmth
Need help pls

a.) Show that for any polynomial f(x) there exists a polynomial g(x) such that
f(x) = x*g(x) + c, where c is a constant.

b.) Use the result in letter a.) and the remainder theorem to prove the factor theorem.

Let $f(x) = a_nx^n+...+a_1x+a_0$ then $f(x) = xg(x)+a_0$ where $g(x) = a_nx^{n-1}+...+a_1$.