I'm working through a book and reached the result below. Verying the truth of the statement is claimed to be easy but I've had little luck. Any ideas how to proceed?
Let f(x) be a monic polynomial in Q[x] of degree n where n happens to be even. Then there exist polynomials g(x) and h(x) such that f(x)=g(x)^2-h(x) and g(x) has degree 1/2*n and h(x) has degree at most 1/2*n-1.