Problem: If f(x)=5x2−2x−1f(x)=5 x^{2}-2 x-1f(x)=5x2−2x−1, then f(x+h)−f(x)f(x+h)-f(x)f(x+h)−f(x) equals:
Answer Choices:
A. 5h2−2h5 h^{2}-2 h5h2−2h
B. 10xh−4x+210 x h-4 x+210xh−4x+2
C. 10xh−2x−210 x h-2 x-210xh−2x−2
D. h(10x+5h−2)h(10 x+5 h-2)h(10x+5h−2)
E. 3h3 h3h Solution:
f(x+h)−f(x)=5(x+h)2−2(x+h)−1−(5x2−2x−1)f(x+h)-f(x)=5(x+h)^{2}-2(x+h)-1-\left(5 x^{2}-2 x-1\right) f(x+h)−f(x)=5(x+h)2−2(x+h)−1−(5x2−2x−1)
=10xh+5h2−2h=h(10x+5h−2).=10 x h+5 h^{2}-2 h=h(10 x+5 h-2) . =10xh+5h2−2h=h(10x+5h−2).