Question

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

Answer 1

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^3-5x+3~=(x+2.4908)(x-1.8342)(x-0.6566)`

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!