If f(x) = 5x^2 - 2x - 1, then f(x + h) - f(x) equals:

smc

algebra intermediate

Problem

f (x) = 5 x^{2} - 2 x - 1

, then

f (x + h) - f (x)

equals:

(A)

5 h^{2} - 2 h

(B)

10 x h - 4 x + 2

(C)

10 x h - 2 x - 2

(D)

h (10 x + 5 h - 2)

Solution

5 (x + h)^{2} - 2 (x + h) - 1 - (5 x^{2} - 2 x - 1) ⟹ 5 (x^{2} + 2 x h + h^{2}) - 2 x - 2 h - 1 - 5 x^{2} + 2 x + 1 ⟹ 10 x h + 5 h^{2} - 2 h

⟹ h (10 x + 5 h - 2) h (10 x + 5 h - 2)

Final answer