Find all the roots of the equation. Show your step-by-step work. x^3−x^2−x−2=0
MAKE THE ANSWER SHORT AND SIMPLE
To find the roots of the equation x^3 - x^2 - x - 2 = 0, we can use synthetic division or guess and check to find one root, and then use polynomial long division or synthetic division to factorize the equation and find the remaining roots.
Using synthetic division or by guessing and checking, we find that x = -1 is a root of the equation.
Dividing the equation x^3 - x^2 - x - 2 by (x + 1) using polynomial long division or synthetic division, we get (x + 1)(x^2 - 2x - 2) = 0.
To solve x^2 - 2x - 2 = 0, we can either factorize it or use the quadratic formula.
Factoring the quadratic equation, we get (x - 2)(x + 1) = 0.
So, the roots of the equation x^3 - x^2 - x - 2 = 0 are x = -1, x = 2, and x = -1.