Factor By Grouping 3rd Degree Polynomial

Question

Just to be upfront, this is a homework question, I already know the answer, but I can't figure out how to get there or the logic behind the hint, which is really what I'm after. Please don't solve it for me, just give me some pointers in the right direction or links to better instructions.

The problem:

Factor the expression $x^3 - 3x^2 + 4$

The hint the book provides "subtract and add 1, then factor by grouping"

The given answer is $(x+1)(x-2)^2$

Answer 1

HINT

$x^3 - 3x^2 + 4 = x^3 + 1 -3x^2 + 3 = (x + 1)(...) - 3(x^2 - 1) = ...$

Answer 2

Hint: use @pedja,s hint (this is the best, I can think of).

Else, split $4$ as $4=3+1$ and go through a longer route.