How to Factor a longer polynomial for Calc

Question

So I'm working on a Calc problem and have to factor the following:

$ 12\left(x^3-x^2-x+1\right) $

This is Calc 1. I've factored quite a bit in algebra and calculus, but nothing like this. My professor ended up getting:

$ 12\left(x+1\right)\left(x-1\right)^2 $

...and I have no idea how. Is there a procedure I should know of, a rule for this sort of polynomial?

Answer 1

$$12\left(x^3-x^2-x+1\right)=12\left((x^3-x^2)-(x-1)\right)=12(x^2(x-1)-(x-1))$$ $$=12(x-1)(x^2-1)$$ $$=12(x-1)(x-1)(x+1)=12(x-1)^2(x+1)$$

Answer 2

"Grouping": \begin{align} x^3 - x^2 - x + x & = \Big(x^3 - x^2\Big) - \Big(x-1\Big) \\[10pt] & = x^2 \Big(x-1\Big) - 1\Big(x-1\Big) \\[10pt] & = (x^2-1)(x-1) \\[10pt] & = \cdots \end{align}