Intermediate Algebra for College Students (7th Edition)

$h^2+2ah-5h$
Given: $f(x)=x^2-5x+3$ and $f(a)=a^2-5a+3$ Now, we will have to solve. $f(a+h)-f(a)=[(a+h)^2-5(a+h)+3]-(a^2-5a+3)$ This gives $=a^2+h^2+2ah-5a-5h+3-a^2+5a-3$ or, $=h^2+2ah-5h$