# Working on a polynomial

1. Oct 21, 2008

### Kushal

1. The problem statement, all variables and given/known data

when the polynomial f(x) is divided by (x-1) the remainder is 2, and when f(x) is divided by (x-3) the remainder is 4. Find the remainder when f(x) is divided by x2 - 4x + 3.

3. The attempt at a solution

i thought of adding the remainders since x2 - 4x + 3 = (x-1)(x-3) but that wouldn't sound very logical.....:S

2. Oct 21, 2008

### Tedjn

Re: polynomial!!!

What is the degree of the remainder of f(x) divided by x2 - 4x + 3?

3. Oct 21, 2008

### Kushal

Re: polynomial!!!

ermm well it will be in the form (x + a)

but how do i find a?

4. Oct 22, 2008

### Tedjn

Re: polynomial!!!

While it is true in this case that the remainder is of the form x + a, I think it is usually the case that the remainder is in the form ax + b. How would you find this exactly? Well, consider that f(x) = (x-1)p(x) + 2 = (x-3)q(x) + 4 = (x-1)(x-3)s(x) + (ax+b). What do you get if you plug in f(1) and f(3)?

5. Oct 22, 2008

### Kushal

Re: polynomial!!!

i would get 2 equations for ax+b.

then i'll be able to solve for a and b simultaneously......:)

i hope this is correct.

thnks