Question

Factor this polynomial completely over the set of complex numbers.
x^3-x^2-4x+4

Answer 1

by inspection of the coefficients, 1 is a zero, so x - 1 is a factor

x^3 - x^2 - 4x + 4 = (x - 1)(x^2 - 4)
you can factor by grouping:
x^2 (x - 1) - 4(x - 1) = (x - 1)(x^2 - 4)
and x^2 - 4 = (x - 2)(x + 2)

fully factored: (x - 1)(x - 2)(x + 2)
zeros: 1 , 2 , -2
all three zeros are real (or complex with an imaginary component of 0)