factoring equations

Question

Let f(x)=-5x^2+7x+5. Find f(x+h)-f(x). 

f(x+h)-f(x)=____. 

(Simplify your answer.) 

Answer 1

f(x + h) = -5(x + h)² + 7(x + h) + 5 = -5x² - 10xh - 5h² + 7x + 7h +5

f(x) = -5x² + 7x + 5

 

f(x + h) - f(x) = -5x² - 10xh - 5h² + 7x + 7h +5 + 5x² - 7x - 5

= -10xh - 5h² + 7h = h(5h - 10x + 7)