find all zero's for 2x^4-11x^3+16x^2-x-6
im needing the complex, rational, irrational, and all of the zero's
I tried synthetic division and fortunaltely it worked nicely for x = 1,2, and 3
so we know that (x-1)(x-2)(x-3) are factors
so we can "reason" out what the fourth factor has to be
at the front so far we have x^3 but we need 2x^4, so the start of the missing factor is 2x
at the end so far we have (-1)(-2)(-3) or -6 so we need +1 at the end of our factor
missing factor is (2x+1)
2x^4-11x^3+16x^2-x-6 = (x-1)(x-2)(x-3)(2x+1)