Question from Sasha, a student:

Simplify the difference quotient

f(x) − f(a)/ x-a if x ≠ a. f(x) = x^3 − 12

I thought I had gotten the answer right at x^2+a^2 but it is wrong. My work is below, can you help?

f(x)=(x^3-12)-(a^3-12)/x-a f(x)=x^3-a^3/x-a f(x)=x^3+a^3

Hi Sasha,

When you have

\[\frac{x^3 - a^3}{x - a}\]

you need to factor the numerator as the difference of cubes.

Penny