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

1954 AMC 12 Problem 16

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16.

f(x)=5x^2-2x-1,

then

f(x+h)-f(x)

equals:

5h^2-2h

10xh-4x+2

10xh-2x-2

h(10x+5h-2)

3h

Substitute

x+h

into the polynomial before subtracting

f(x)

After cancellation, factor out

h

Expanding and canceling gives

\begin{gathered} f(x+h)-f(x)\\ =5(x+h)^2-2(x+h)-1\\ {}-(5x^2-2x-1)\\ =10xh+5h^2-2h\\ =h(10x+5h-2). \end{gathered}

Thus, the correct answer is D.