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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
