# Math Help - Division in Polynomial Rings

1. ## Division in Polynomial Rings

I'm having troubles with this problem

Let $F$ be a Field, and suppose that $a\in F$ and $f(x)\in F[x]$. Show $f(a)$ is the remainder when $f(x)$ is divided by $x-a$

The case when $f(a)=0$ is trivial but I don't know what to do from there.

2. Originally Posted by Haven
I'm having troubles with this problem

Let $F$ be a Field, and suppose that $a\in F$ and $f(x)\in F[x]$. Show $f(a)$ is the remainder when $f(x)$ is divided by $x-a$

The case when $f(a)=0$ is trivial but I don't know what to do from there.
If q(x) is the quotient and r is the remainder when f(x) is divided by x–a then, by definition, f(x) = (x–a)q(x) + r. Now all you have to do is to put x=a.

3. That is so simple, I can't believe I didn't get that.