Hi,

I'm to find the GCD of two polynomials, f(x) and g(x) in the field of integers mod 5, and then write it as a linear combination using the polynomials.

$\displaystyle

f(x)=x^2 +2$ and $\displaystyle g(x)=x^3+4x^2+x+1$

I've found that the gcd $\displaystyle = 1 = (x^2 + 2) - [(-x +3)(-x+2)]$

What does this mean?? Certainly the gcd is 1, but what is the right hand?
but I'm having a lot of trouble turning that into the correct answer which is:

$\displaystyle (4x^2 + 3x + 4)(f(x) - (4x +2)g(x))$.

Did I make a mistake somewhere? Thanks for any help.