little bit confused- how come you used -1 in f(x)? im struggling to see how you factorised and simplified it. sorry im a bit slow with maths could you explain it a bit more?
I'm adding to Tapioca's explanation since it seems like you may not have covered the polynomial theorem in school yet which teaches that if f(a) = 0 then (x -a) is a factor of f(x). It's common to test easy numbers first (like 1, -1, 2, -2) when trying to find the first factor.
It might be easiest to first see this looking from the other perspective.
if you have (x-a)(x-c)(x-d) then we know we can make the whole thing = 0 by making one of the brackets equal zero. (null factor law).
I.e. if (x-a) is a factor, then making x = a means that the equation equals zero.
So to restate, Tapioca was using the similar idea that if have x = a makes the whole thing equal zero, then that means (x-a) is a factor.
That's the first step. The 2nd step may also be a bit tricky but before we move on I think it's important to check that you get the first one
Kudos to you for reaching out for help and to Tapioca for the explanations