# How do you factor x^3+x^2-5x+3?

May 30, 2015

First notice that $x = 1$ is a solution of ${x}^{3} + {x}^{2} - 5 x + 3 = 0$

So $\left(x - 1\right)$ is a factor.

Let's use synthetic division to find.

${x}^{3} + {x}^{2} - 5 x + 3 = \left(x - 1\right) \left({x}^{2} + 2 x - 3\right)$

Notice that $x = 1$ is a root of ${x}^{2} + 2 x - 3 = 0$

So there's another factor $\left(x - 1\right)$

${x}^{3} + {x}^{2} - 5 x + 3 = \left(x - 1\right) \left(x - 1\right) \left(x + 3\right)$