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Spain Mathematical Olympiad
1984 Spain Mathematical Olympiad
8
8
Part of
1984 Spain Mathematical Olympiad
Problems
(1)
find the remainder upon division by x^2-1 of the 4x4 determinant ...
Source: Spanish Mathematical Olympiad 1984 P8
8/3/2018
Find the remainder upon division by
x
2
−
1
x^2-1
x
2
−
1
of the determinant
∣
x
3
+
3
x
2
1
0
x
2
+
5
x
3
0
2
x
4
+
x
2
+
1
2
1
3
x
5
+
1
1
2
3
∣
\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}
x
3
+
3
x
x
2
+
5
x
x
4
+
x
2
+
1
x
5
+
1
2
3
2
1
1
0
1
2
0
2
3
3
remainder
polynomial
Determinants
algebra