Question

Factor

x^3-x^2-x+1

I got the first part I think but don't know what to do with the -x

X^2(x-1) ?

@ precal

Answer 1

use factor theorem:

if f(a) = 0 then (x-a) is a factor

f(1) = 0 hence (x-1) is a factor

(x-1)(ax^2 + bx + c)

we can see that a = 1 ( to get x^3) and c = -1 (to get 1)

(x-1)(x^2 + bx -1) = x^3-x^2-x+1

compare coefficients of x:

-b - 1 = -1

therefore b = 0

now difference of two squares applies to what we have left:
(x^2 -1)(x-1) = (x+1)(x-1)(x-1) = (x+1)(x-1)^2