Chapter 4 - Section 4.3 - Polynomial Functions, Graphs, and Composition - 4.3 Exercises - Page 295: 22

a. $-x^{2}-7x+22$, b. $7x^{2}-11x-2$

We are given that $f(x)=3x^{2}-9x+10$ and $g(x)=-4x^{2}+2x+12$. We know that $(f+g)(x)=f(x)+g(x)$ and $(f-g)(x)=f(x)-g(x)$. Therefore: $(f+g)(x)=(3x^{2}-9x+10)+(-4x^{2}+2x+12)=3x^{2}-4x^{2}-9x+2x+10+12=-x^{2}-7x+22$. $(f-g)(x)= (3x^{2}-9x+10)-(-4x^{2}+2x+12)=3x^{2}+4x^{2}-9x-2x+10-12=7x^{2}-11x-2$