Question

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

Answer 1

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.