Given polynomial is f(x)=x5+9x4+12x2+6 .
Compare the polynomial with f(x)=a5x5+a4x4+a3x3+a2x2+a1x+a0 , we have
a5=1,a4=9,a3=0,a2=12,a1=0,a0=6 .
There esist a prime number p=3 which divides all coefficients a4,a3,a2,a1,a0 , but not the leading coefficient a5 and, p2 not divide the constant term .
Hence, using the Einstein Criteria, given polynomial is irreducible over Q .
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