Factor the polynomial and use the factored form to find the real zeros. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)

Question

P(x) = x³ + x² − x − 1

*My answer was: -1,1. That was incorrect

Answer 1

P(x) = x³ + x² − x − 1

= x²(x+1) - (x+1)

= (x+1)(x² - 1)

= (x+1)(x - 1)(x + 1)

= (x - 1)(x+1)²

= 0 when x = 1 or -1 with -1 as double root.

Answer: -1, -1, 1

The reason that 1, -1 is wrong is that there are three roots to cubic equations, not two.