Complex zeros and factored form

Question

x³-5x²+12x-8

find the complex zeros and write in factored form

Answer 1

First guess to find a root. If you plug in x=1 you will find that this is a root. So (x-1) is a factor to your expression. Do long division on your initial expression by (x-1). Then your factors will be (x-1) and whatever you get from long division. But your answer from long division will be quadratic. You can factor the quadratic expression as usual. The factors to your quadratic and (x-1) will be all the factors you need. From there, it should be straightforward to find the zeros.