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

1 Answer
Jun 12, 2015

Answer:

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!