Show that $X^5+X^3+1$ is irreducible over $\mathbb{Z}$ and $X^3+aX^2+bX+1$ is reducible iff $a=b$ or $a+b=-2$.
(Ir)reducible polynomial over $\mathbb{Z}$
-1
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abstract-algebra
ring-theory
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3What do you mean "irregularly polynomial"? Perhaps you meant "irreducible polynomial"? – 2012-12-25
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0ok, sorry anyone – 2012-12-25
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0I think you might have the conditions on $X^3+aX^2+bx+1$ backwards - this polynomial is *reducible* iff $\dots$ – 2012-12-25