suppose we COULD.

we then have 1 = 2f(x) + xg(x), for some polynomials f(x),g(x) in Z[x].

suppose that deg(f) = m, and deg(g) = n. let k = max(m,n). then we can write:

(some of the coefficients may be 0).

then:

.

since these are equal polynomials, we must have equal constant terms, so for some integer , which cannot happen.