# How do you use the rational roots theorem to find all possible zeros of x^3 + 3x^2 - x - 3?

Feb 27, 2016

Zeros are $- 1. 1$ and $- 3$

#### Explanation:

To find all possible zeros of x^3+3x^2−x−3, we find rational roots of equation x^3+3x^2−x−3=0. Factorizing

x^3+3x^2−x−3=0

= ${x}^{2} \left(x + 3\right) - 1 \left(x + 3\right)$

= $\left({x}^{2} - 1\right) \left(x + 3\right)$

= $\left(x + 1\right) \left(x - 1\right) \left(x + 3\right)$

Hence zeros are given by $x + 1 = 0$, $x - 1 = 0$ and $x + 3 = 0$ i.e.

Zeros are $- 1. 1$ and $- 3$