Question 1148163
<br>
By trial and error with from a list of the possible rational roots -- or, much better, by finding the roots with a graphing calculator -- determine that one root is -5.  Then reduce the polynomial using synthetic division.<br><pre>

    -5  |  6  25  -24   5
        |    -30   25  -5
        +-----------------
           6  -5    1   0</pre>
So<br>
{{{6x^3+25x^2-24x+5 = (x+5)(6x^2-5x+1)}}}<br>
Then the quadratic factors nicely:<br<
{{{6x^3+25x^2-24x+5 = (x+5)(3x-1)(2x-1)}}}<br>
And so the roots are -5, 1/3, and 1/2.<br>