Question 31023: Determine if the polynomial is irreducible over Q(rationals)
127t^5 - 5t - 7
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! SEE THE FOLLOWING AND TRY
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127t^5 - 43t^2 + 7=F(T)
FIND FACTORS FOR CONSTANT TERM ...THEY ARE 1,-1,7 AND -7......CALL THIS N
FIND FACTORS FOR HIGHEST DEGREE TERM..THEY ARE 1,-1,127,-127....CALL THIS...D
RATIONAL ROOTS COULD THEN BE ONLY FROM N/D...THAT IS
1/1=1......1/-1=-1........1/127......1/-127
7/1=7......7/-1=-7........7/127......7/-127
THAT IS ALL......... SO TEST EACH OF THEM IN THE GIVEN EQN. TO FIND IF IT GIVES A ZERO..THEN IT IS REDUCIBLE OTHERWISE NOT
WE FIND THAT F(T) IS NOT ZERO FOR ANY OF THESE VALUES..SO IT IS IRREDUCIBLE OVER Q(RATIONAL)
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