SOLUTION: factor the polynomial completely x^3+8X^2+19X+12

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Question 331322: factor the polynomial completely x^3+8X^2+19X+12
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
factor the polynomial completely 

All feasible rational zeros are  the factors of 12 


 , , , , , ,   

Also there are no sign changes so there are no positive zeros.

So we begin by trying -1


 -1| 1  8 19  12
   |   -1 -7 -12
     1  7 12   0

So x = -1 is a zero, so therefore (x + 1) is a factor.
So now we have factored the original polynomial as





Now we factor the trinomial on the right and get:



That's it.

Edwin
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