Question 1127451
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Show that the given values are zeros of P(x) and find all other zeros. 

P(X)=3x^4-8x^3-14x^2+31x+6    Values: -2 and 3
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<pre>

-2   |   3   -8   -14   31    6
     |
     |       -6    28  -28    -6
     |____________________________
         3  -14    14    3    0      -----remainder 0,  root:   -2


3   |   3   -14   14   3
    |
    |        9    -15  -3
    |______________________    
       3     -5   -1   0    ---------remainder 0, root:  +3
</pre>

{{{P(x)=(x+2)(x-3)(3x^2-5x-1)}}}


The quadratic roots

{{{(5+- sqrt(25+12))/6}}}


These other two roots are therefore irrational,
{{{(5-sqrt(13))/6}}}
{{{and}}}
{{{(5+sqrt(13))/6}}}