If fx x5 2x3 x2 2x 3 gx x4 x3 4x2 3x 3 then find

Question

If f(x) = x^5 + 2x^3 + x^2 + 2x + 3, g(x) = x^4 + x^3 + 4x^2 + 3x + 3, then find greatest common divisor of f(x) and g(x) over the field of residue classes modulo 5 and express it in the form

d(x) = m(x) f(x) + n(x) g(x) where d(x) = g.c.d. of f(x) and g(x).