Question

what is/are the x-intercepts of f(x)=x^3-3x^2+4

Answer 1

well by observation I'd say one is x = -1

when you use the factor theorem you get

f(-1) = (-1)^3 - 3(-1)^2 + 4 = 0

so then you can do some polynomial division or synthetic division to and look at the quadratic factor

an alternative is to look at the rational root theorem

find the factors of 4 call them q the constant

and 1 call them p the coefficient of the leading term

and any ratio roots will be q/p

hope it helps