# The Remainder Theorem and The Factor Theorem

1. Jun 11, 2009

### Stratosphere

1. The problem statement, all variables and given/known data
I understand How to do The remainder Theorem and The factor Theorem but I don't understand what they mean or what they are doing. I don't think I will be able to apply them without knowing what they mean. Can someone explain them to me?

2. Relevant equations

3. The attempt at a solution

2. Jun 11, 2009

### rock.freak667

The theorem is basically this, if f(x) is any polynomial and f(x) is divided by x-a, then the remainder is f(a) [remainder theorem]. If f(a)=0 then x-a is factor of f(x) [factor theorem]

so basically when you divide f(x) by x-a, you will get a polynomial p(x) and a remainder R. So you can rewrite f(x) as such

f(x)=p(x)*(x-a)+R

clearly you can see why, the remainder is f(a).
You can also see that when f(a)=0, the remainder R=0 as well. This can only happen when you divide by a factor.

I hope this explained it better for you.