Consider the polynomials
f(x) = 1 - 12x + 3x^2 - 4x^3 + 5x^4
g(x) = 3 - 2x - 6x^3+ 10x^4
Find c such that the polynomial f(x) + cg(x) has degree 3.
If c = -1/2 the 10x^4 in g(x) will become -5 x^4 and will cancel the 5x^4 in f(x) leaving a polynomial of degree 3 when the f(x) and c (g(x) are added.