Factor the polynomial function over the complex numbers. f (x) = x^3-3x^2+2x-6

This one's kinda tricky

Start by putting parenthesis around the first two terms and last two terms

(x^3 - 3x^2) + (2x - 6)

Now, see what you can pull out.

In the first set, you can see they have an x^2 in common.

In the second set, they have a factor of 2 in common.

Therefore,

x^2 (x - 3) + 2 (x - 3)

combine the like terms to get

(x^2 + 2) (x - 3)