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.
Since right now, f(x) has a degree of 4, (6x^4), cg(x) needs to have -6x^4 to balance it out.
g(x) already has 9x^4, but it needs to be -6x^4, so you multiply by -2/3.
Yeah....that would have been my guess too, catmg
But....look what happens
(1 - 12x + 3x^2 - 4x^3 + 6x^4 ) - (2/3) ( 3 - 2x - 6x^3 + 9x^4 ) =
3x^2 - (32/3)x - 1
We cancel the x^4 and x^3 terms
So....I don't believe there is a "c" that we can find to leave a 3rd power polynomial