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A nonconstant polynomial B is said to divide a polynomial A if there exists a nonconstant polynomial Q such that \(A(x) = B(x)Q(x)\) . The polynomials B and Q are then called divisors or factors of A.Divisors FactorsFor example, \(3x+2\) and \((4x-1)\) divide \(12x^2 + 5x - 2\) since \(12x^2 + 5x - 2 = (3x+2)(4x-1)\) . We exclude constant polynomials from these definitions to avoid trivialities.

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Polynomial Divisibility and Roots

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  • 发表日期：

    2025年

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  • Hugo D. Junghenn

摘要

A nonconstant polynomial B is said to divide a polynomial A if there exists a nonconstant polynomial Q such that \(A(x) = B(x)Q(x)\) . The polynomials B and Q are then called divisors or factors of A.Divisors FactorsFor example, \(3x+2\) and \((4x-1)\) divide \(12x^2 + 5x - 2\) since \(12x^2 + 5x - 2 = (3x+2)(4x-1)\) . We exclude constant polynomials from these definitions to avoid trivialities.