Answer
(a) $x^2+2xh+h^2+3x+3h+1$
(b) $2xh+h^2+3h$
(c) $2x+h+3$
Work Step by Step
(a) Given $f(x)=x^2+3x+1$, we have $f(x+h)=(x+h)^2+3(x+h)+1=x^2+2xh+h^2+3x+3h+1$
(b) $f(x+h)-f(x)=x^2+2xh+h^2+3x+3h+1-(x^2+3x+1)=2xh+h^2+3h$
(c) $\frac{f(x+h)-f(x)}{h}=2x+h+3$