Originally Posted by

**LJoe21** Hello there,

I need to find the polynomials $\displaystyle f(x)$ and $\displaystyle g(x)$, which are of the *lowest possible degree* and *satisfy the given condition*:

$\displaystyle (x^4-2x^3-4x^2+6x+1) \cdot f(x) + (x^3-5x-3) \cdot g(x) = x^4$

All I want to know is how to find **the lowest possible degree** that the polynomials should be of. I can solve the rest using the method of undetermined coefficients—but if there's another way (preferably easier), then feel free to share.

This is my first post here, so please bear with me if I did anything wrong.

Thanks in advance.