Sally is given the information ƒ (1) = 0, ƒ (-2) = 0 and ƒ (3) = 0. which are the factors of the polynomial?

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.