Difference Quotient for f(x) = 3x^2 + x - 3

[as8906]

If f(x) = 3x2 + x – 3, find [f(x) - f(a)]/(x-a). Here is all the work I have done:

(x)-f(a)=( 3x2 + x – 3)-( 3a2 + a – 3) = 3x2 + x – 3 - 3a2 - a + 3 = 3x2 - 3a2+ x-a = 3(x2 - a2) +x – a =3(x+a)(x-a)+(x-a)

I know that the next step is this:

3(x+a)(x-a)+(x-a) = (x-a)(3x+3a+1)

But I don't understand how it goes from 3(x+a)(x-a)+(x-a) to (x-a)(3x+3a+1). I just need someone to explain the method used to solve this one step. The remainder of the problem can be easily taken care of. Any help would be appreciated.

 

[Denis]

Re: Difference Quotient

3(x+a)(x-a)+(x-a) = (x-a)(3x+3a+1)
But I don't understand how it goes from 3(x+a)(x-a)+(x-a) to (x-a)(3x+3a+1).

3(x+a)(x-a)+(x-a)
(x-a) is common, so:
(x-a)[3(x+a) + 1] : kapish?