math
posted by Joe .
find all zero's for 2x^411x^3+16x^2x6
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 (x1)(x2)(x3) 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^411x^3+16x^2x6 = (x1)(x2)(x3)(2x+1)