Polynomial irreducible $\implies $ "Reverse" polynomial irreducible

Asked Nov 17 '19 at 16:52

Active Nov 17 '19 at 16:58

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If $$a_nx^n+\cdots +a_0$$ is irreducible over some field, the polynomial $$a_0x^n+\cdots +a_n$$ with the coefficients reversed is irreducible over the same field as well.

Suppose the polynomial can be expressed as product of two polynomial the original polynomial will be reduced. Thats what I want to do but I ran out of idea. can someone help me?

edited Nov 17 '19 at 16:58

Peter

84,454

asked Nov 17 '19 at 16:52

Mady

4

Hint: if $p(x)$ is the given polynomial, then the "reverse" polynomial is given by $x^np\left( \frac 1x\right)$. – lulu Nov 17 '19 at 16:53
@lulu: I think you can make this an answer. – RghtHndSd Nov 17 '19 at 17:01
Can u explain further? – Madhan Kumar Nov 17 '19 at 17:01

Polynomial irreducible $\implies $ "Reverse" polynomial irreducible

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