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.
We need to have the x^4 terms 'cancel out' to end with a degree 3 polynomial
c * 5x^4 + 19x^4 = 0
c = - 19/5
so the polynomial could be anything with -19/5 x^4 in it ( and no higher degree term in it...and also, don't 'cancel out the x^3 terms)
- 19/5 x^4 + x^3 - x^2 + 4 x + 10 would be an example....