Editing Reciprocal polynomial (section)

== Properties ==
Reciprocal polynomials have several connections with their original polynomials, including:
# {{math|1=deg ''p'' = deg ''p''<sup>∗</sup> if <math>a_0</math> is not 0.}}
# {{math|1=''p''(''x'') = ''x''<sup>''n''</sup>''p''<sup>∗</sup>(''x''<sup>−1</sup>)}}.<ref name="Aigner"/>
# For {{math|''α''}} is a [[zero of a function|root]] of a polynomial {{math|''p''}} if and only if {{math|''α''<sup>−1</sup>}} is a root of {{math|''p''<sup>∗</sup>}} or if <math> \alpha = 0 </math> and <math> p ^* </math> is of lower degree than <math> p </math>.<ref name="Pless 1990 loc=pg. 57">{{harvnb|Pless|1990|loc=pg. 57}}</ref>
# If {{math|''x'' ∤ ''p''(''x'')}} then {{math|''p''}} is [[Irreducible polynomial|irreducible]] if and only if {{math|''p''<sup>∗</sup>}} is irreducible.<ref name="Roman 1995 loc= pg. 37">{{harvnb|Roman|1995|loc= pg. 37}}</ref>
# {{math|''p''}} is [[Primitive polynomial (field theory)|primitive]] if and only if {{math|''p''<sup>∗</sup>}} is primitive.<ref name="Pless 1990 loc=pg. 57"/>

Other properties of reciprocal polynomials may be obtained, for instance:
* A self-reciprocal polynomial of odd degree is divisible by x+1, hence is not irreducible if its degree is > 1.