Use the rational roots theorem to write the function in factored form and find all zeros.?

Question

P(x)= x^3-2x^2-16x+32

Answer 1

The rational roots theorem tells us that any zero of
P(x) must divide 32. By trial, we see that 2 is
a zero of P(x). So x-2 is a factor. By synthetic
division or long division, the quotient is x²-16.
So we have
(x-2)(x-4)(x+4) = 0
and the zeros of P(x) are -4, 2 and 4.