Question

Factor polynomial x^3+x^2-x-1

Answer 1

To factor the polynomial x^3 + x^2 - x - 1, we can use synthetic division or guess and check.

One possible way to factor it is:

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

Now let's continue factoring the quadratic term:

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

So the factored form of the polynomial is:

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

Therefore, the polynomial x^3 + x^2 - x - 1 factors as (x + 1)(x + 1)(x - 1).