Fully factorise

Question

X^3-4x^2+x-6

I got (x+3) as a factor but I'm not sure what the other two factors are.

Please help

Thankyou

Answer 1

Doing your division, I get a remainder of -72, so x+3 is not a factor.

I found that x^3-4x^2+x-6 has no rational roots at all!

So, I suspect a typo in the problem, if you were expected to factor it.

I did find that

x^3-4x^2+x+6 = (x+1)(x-2)(x-3)