If $f(x)$ and $g(x)$ are polynomials such that $f(x) + g(x) = -2 + x,$ then what is $g(x)$ if $f(x) = x^3 - 2x - 2$?
We have that
f(x) + g(x) = x - 2 and so
[ x^3 - 2x - 2 ] + g(x) = x - 2 subtract x^3 from both sides...add 2x, 2 to both sides
g(x) = -x^3 + 3x
+1242 
