Answer
$3x^2+3hx+h^2-10x-5h+1$
Work Step by Step
$f(x)=x^3-5x^2+x$
$\frac{f(x+h)-f(x)}{h}=\frac{((x+h)^3-5(x+h)^2+(x+h))-(x^3-5x^2+x)}{h}$
$=\frac{(x^3+3x^2h+3xh^2+h^3-5(x^2+h^2+2xh)+x+h)-(x^3-5x^2+x)}{h}$
$=\frac{3x^2h+3h^2x+h^3-10hx-5h^2+h}{h}$
$=3x^2+3hx+h^2-10x-5h+1$
