If f(x) and g(x) are polynomials such that f(x)+g(x)=−2+x, then what is g(x) if f(x)=x3−2x−2?
Solution — click to reveal
We substitute f(x)=x3−2x−2 into f(x)+g(x)=−2+x to find that (x3−2x−2)+g(x)=−2+x. Then, g(x)=−2+x−(x3−2x−2). Distributing, we find g(x)=−2+x−x3+2x+2=−x3+3x.