Consider the polynomials f(x)=1-12x+3x^2-4x^3+6x^4 and g(x)=3-2x-6x^3+9x^4.
Find c such that the polynomial f(x) + cg(x) has degree 3.
You want the x^4 terms to cancel out, so you have -9c=6 -> c = -6/9 = -2/3
-2/3