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find the remainder upon division by x^2-1 of the 4x4 determinant ...

Source: Spanish Mathematical Olympiad 1984 P8

August 3, 2018

remainderpolynomialDeterminantsalgebra

Problem Statement

Find the remainder upon division by

x^2-1

of the determinant

\begin{vmatrix} x^3+3x & 2 & 1 & 0 \\ x^2+5x & 3 & 0 & 2 \\x^4 +x^2+1 & 2 & 1 & 3 \\x^5 +1 & 1 & 2 & 3 \\ \end{vmatrix}