# How do you factor #y= 6x^3+13x^2-14x+3# ?

##### 1 Answer

#### Explanation:

We can optimistically hope that

has at least one rational root.

By the Rational Root Theorem we know that any such root must be of the form

where

and

There turn out to only be 10 possible rational roots using this information:

You could evaluate these manually, but I used a spreadsheet:

In this case, we have been extremely lucky, since we have all 3 possible roots identified

Which implies the factors:

or (after using the