Polynomials

Reciprocal polynomial

In algebra, given a polynomial with coefficients from an arbitrary field, its reciprocal polynomial or reflected polynomial, denoted by p∗ or pR, is the polynomial That is, the coefficients of p∗ are the coefficients of p in reverse order. They arise naturally in linear algebra as the characteristic polynomial of the inverse of a matrix. In the special case where the field is the complex numbers, when the conjugate reciprocal polynomial, denoted p†, is defined by, where denotes the complex conjugate of , and is also called the reciprocal polynomial when no confusion can arise. A polynomial p is called self-reciprocal or palindromic if p(x) = p∗(x).The coefficients of a self-reciprocal polynomial satisfy ai = an−i for all i. (Wikipedia).

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Classify a polynomial then determining if it is a polynomial or not

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From playlist Is it a polynomial or not?

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From playlist Summer of Math Exposition 2 videos

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Classify a polynomial and determine degree and Leading coefficient

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Classify a polynomial and determine degree and leading coefficient

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Classify a polynomial and determine degree and leading coefficient

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Related pages

Palindrome | Primitive polynomial (field theory) | Cyclic code | Characteristic polynomial | Linear algebra | Coefficient | Zero of a function | Derivative | Minimal polynomial (field theory) | Special number field sieve | Polynomial | Euler's totient function | Unit disk | Algebra | Degree of a polynomial | Cohn's theorem | Complex plane | Monic polynomial | Binomial coefficient | Characteristic (algebra) | Unit circle | Field (mathematics) | Integer | Real number | Multiplicity (mathematics) | Complex conjugate | Cyclotomic polynomial | Irreducible polynomial | Parity (mathematics) | Complex number | Orthogonal complement