# Thread: Polynomials Divison and remainder

1. ## Polynomials Divison and remainder

I have don't understand how to solve problems like this:
When we divide f(x) by (x-1), (x-2) and (x+1) the remainders are 3, 7 and 5. Find the remainder of f(x) divided by (x-1)(x-2)(x+1).

I try to write them like this:
f(x) = P*(x-1)+3
f(x) = Q*(x-2)+7
f(x) = R*(x+1)+5
To get a result like this after some manipulation:
f(x) = S*(x-1)*(x-2)*(x+1)+y
But I can't.

2. The first thing you should note, from the remainder theorem, is that

$f(1) = 3, f(2) = 7, f(-1) = 5$.

Are you told what degree the polynomial is?

3. Originally Posted by Prove It
The first thing you should note, from the remainder theorem, is that

$f(1) = 3, f(2) = 7, f(-1) = 5$.

Are you told what degree the polynomial is?
No, That is the complete problem.