# How do you factor x^3 + x^2 + x - 3?

Nov 22, 2015

First, you know that $x = 1$ is a root because ...

$1 + 1 + 1 - 3 = 0$

#### Explanation:

So, divide the function by $\left(x - 1\right)$ using synthetic or long division to get ...

${x}^{2} + 2 x + 3$

Now, this function has only imaginary roots, so use the quadratic formula ...

$x = \frac{- 2 \pm \sqrt{{2}^{2} - 4 \left(1\right) \left(3\right)}}{2 \left(1\right)} = - 1 \pm i \sqrt{2}$

In summary, here are the factors:

$\left(x - 1\right) \left(x + 1 - i \sqrt{2}\right) \left(x + 1 + i \sqrt{2}\right)$

hope that helped