5 Factorization of polynomials

Polynomial Algorithms in Computer Algebra - Texts and Monographs in Symbolic Computation ◽

10.1007/978-3-7091-6571-3_5 ◽

1996 ◽

pp. 112-150

Author(s):

Franz Winkler

Keyword(s):

Factorization Of Polynomials

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On Ritt's Factorization of Polynomials

Journal of the London Mathematical Society ◽

10.1112/s0024610700001046 ◽

2000 ◽

Vol 62 (1) ◽

pp. 127-138 ◽

Cited By ~ 6

Author(s):

A. F. Beardon ◽

T. W. Ng

Keyword(s):

Factorization Of Polynomials

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Irreducibility testing and factorization of polynomials

10.1109/sfcs.1981.20 ◽

1981 ◽

Cited By ~ 2

Author(s):

Leonard M. Adleman ◽

Andrew M. Odlyzko

Keyword(s):

Factorization Of Polynomials

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Holomorphic factorization of polynomials

Siberian Mathematical Journal ◽

10.1134/s0037446616050153 ◽

2016 ◽

Vol 57 (5) ◽

pp. 860-865

Author(s):

A. L. Pavlov

Keyword(s):

Factorization Of Polynomials

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Factorization of Polynomials

A First Course in Abstract Algebra ◽

10.1201/b17673-8 ◽

2014 ◽

pp. 60-68

Keyword(s):

Factorization Of Polynomials

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5. The algebra of polynomials and cubic equations

Algebra: A Very Short Introduction ◽

10.1093/actrade/9780198732822.003.0005 ◽

2015 ◽

pp. 53-74

Author(s):

Peter M. Higgins

Keyword(s):

Constant Term ◽

Complex Numbers ◽

Distributive Law ◽

Factorization Of Polynomials

Polynomials are expressions of the form p(x) = a0 + a1x + a2x2 + ... + anxn; the number ai is the coefficient of xi, a 0 is the constant term of p(x), and an is the leading coefficient. The underlying algebra of polynomials mirrors that of the integers. Polynomials can be added, subtracted, and multiplied, and the laws of associativity and commutativity and the distributive law of addition over multiplication all hold. Division is more complicated. ‘The algebra of polynomials and cubic equations’ outlines the Remainder and Factor Theorems along with complex numbers in the Argand plane. The factorization of polynomials, the Rational Root Theorem, the Conjugate Root Theorem, and solution of cubic equations are also discussed.

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