PLEASE HELP ME WITH THIS PROBLEM;
fIND ALL ROOTS OF THE POLYNOMIAL X^3 - X^2 + 16X - 16

x³ - x² + 16x - 16

Factor x² out of the first two terms
Factor 16 out of the last two terms

x²(x - 1) + 16(x - 1)

Factor (x - 1) of of these two terms

(x - 1)(x² + 16)

+16 can be written as -16i²

(x - 1)(x² - 16i²)

The second parenthetical expression
is the difference of two squares, and
can be factored thusly

(x - 1)(x - 4i)(x + 4i)

Setting x - 1 = 0 gives 1 as one zero (root).
Setting x - 4i = 0 gives 4i as another zero (root).
Setting x + 4i = 0 gives -4i as the third zero (root).

Edwin