factor x^4-3x^3-11x^2+3x+10 completely using the factor theorem.

Answer 1

using the factor theorem, I tried
x = ±1, ±2, ±5

I found x=1 and x=-1 to work as well as x=-2

so factors would be
(x+1)(x-1)(x+2)(........)

I can reason that the first term of the missing factor is x and it must end in -5

so
x^4-3x^3-11x^2+3x+10
= (x-1)(x+1)(x+2)(x-5)
or
= (x^1 - 1)(x+2)(x-5)