Factor x^3 - 4x^2 + x + 6 with all steps

Answer 1

let f(x) = x^3 - 4x^2 + x + 6
f(1) = 1-4+1+6 ≠0
f(-1) = -1 - 4 -1 + 6 = 0
so (x+1) is a factor

Using synthetic division or long algebraic division
x^3 - 4x^2 + x + 6
= (x+1)(x^2 - 5x + 6)
= (x+1)(x-6)(x+1)

so x = 6 or x = -1 (a double root at x=-1)

Answer 2

thank you!