SOLUTION: factor the polynomial if it cant be factored it is prime 8x^5+16x^4-20x^3+12 please show steps if it can be factored or if prime

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Question 1049369: factor the polynomial if it cant be factored it is prime
8x^5+16x^4-20x^3+12
please show steps if it can be factored or if prime

Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!


All the potential zeros are ± all fractions whose numerators
are divisors of the constant term, 12, and whose denominators 
are divisors of the leading coefficient 8.

The divisors of constant term 12 are (1,2,3,4,6,12}
The divisors of leading coefficient 8 are {1,2,4,8}

The only potential zeros are



and after reducing, we have:



And after eliminating the duplications, the
list shortens to:



We see that the graph only crosses the x axis between -2 and -3,
and -3 is not a zero.  None of the others are between -2 and -3,
so it has no rational zeros, only the irrational one between -2 and
-3.  That means that the polynomial cannot be factored, and is 
therefore prime.

Edwin

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