posted by Kelli .
use the rational zero theorem to find all the zeros of the polynomial function. Use the factor f over the real numbers.
try factors of 12
on the first try, I got f(1) = 0
so x-1 is a factor
by long algebraic or by synthetic division , I got
= (x-1)(x^3 + 3x^2 - 4x - 12)
grouping the x^3 + 3x^2 - 4x - 12
= x^2(x+3) - 4(x+3)
(had I been patient, I would have found
f(2) = 0, f(-3)=0 and f(-2) = 0 as well)
the zeros are
1, 2, -2, -3