f(1) = 0 tells you that wherever you see an x, you put in a one. When you do, the answer comes out as 0
So one of he factors for f(x) is
f(x) = (x -1) * g(x)
If you put an 1 into (x - 1) you get (1 - 1) = 0
The whole thing goes to zero when that happens.
If you split up g(x) so that when x = - 2, the whole polynomial goes to 0 just as what happened with x = 1
f(x) = (x - 1) (x + 2) * h(x)
When x = 3 the same thing happens.
f(x) = (x - 1)(x + 2)(x - 3) and that's your complete answer.
