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

Jun 12, 2015

The easy way is with a calculator that can find roots of polynomials; the hard way is using the cubic formula.

#### Explanation:

If you have a graphing calculator that can find the roots of an equation, you simply plug it in and find the approximate roots. The graph looks like this:

graph{y=x^3-5x+3 [-10,10, -10, 10]}

A solver will give you three roots, approximately:

$x = - 2.4908$
$x = 1.8342$
$x = 0.6566$

So the factorization is approximately:

${x}^{3} - 5 x + 3 \cong \left(x + 2.4908\right) \left(x - 1.8342\right) \left(x - 0.6566\right)$

If you have to do it the hard way, your teacher should have given you the equation (unless you're Good Will Hunting or something). Finis!