Let:
Divide f(x) by g(x) to find:
Verify the remainder is zero in these divisions:
So
Reinsert into the original division:
So
In the ring Q[x], consider the polynomials:
f(x) = x^5 + 2x^3 + x^2 + x + 1 and g(x) = x^4 + x^3 + x -1
a) Find the greatest common divisor d(x) of f(x) and g(x).
b) Find h(x), k(x) element in Q[x] so that h(x)f(x) + k(x)g(x) = d(x)