+230 Consider the polynomials
\[f(x)=1-12x+3x^2-4x^3+5x^4\]
and
\[g(x)=3-2x-6x^3+9x^4.\]
Find $f(x)+cg(x)$ such that the polynomial has degree 3.
+128408 f(x) = 5x^4 -4x^3 + 3x^2 - 12x + 1
g(x) = 9x^4 - 6x^3 - 2x + 3
Really we just want to find a "c" such that
5x^4 + c ( 9x^4) = 0
So getting rid of the "x^4" thingys we have
5 + 9c = 0
9c = - 5
c = -5/9
Proof
5x^4 -4x^3 + 3x^2 - 12x + 1 + (-5/9) [ 9x^4 - 6x^3 - 2x + 3] =
-(2 x^3)/3 + 3 x^2 - (98 x)/9 - 2/3
