Consider the polynomial f(x) = 1 - 12x + 3x^2 - 4x^3 + 5x^4 and g(x) = 3 - 2x - 6x^3 + 19x^4. Find c such that the polynomial f(x) + cg(x) has degree 3.

c * 19 = -5

c = -5/19 Then when multiplied by c the 19x^4 in g(x) becomes -5x^4 which cancels with the 5x^4 if f(x) leaving a polyomial of degree 3