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Kunze Linear Algebra
· Problem 4.4.2
Polynomials
Mathematics — Methods · greatest-common-divisor-polynomials
Problem
Find the g.c.d. of each of the following pairs of polynomials ((a))
2
x
5
−
x
3
−
3
x
2
+
6
x
+
4
,
x
4
+
x
3
−
x
2
−
2
x
−
2
2x^5 - x^3 - 3x^2 + 6x + 4,\quad x^4 + x^3 - x^2 - 2x - 2
2
x
5
−
x
3
−
3
x
2
+
6
x
+
4
,
x
4
+
x
3
−
x
2
−
2
x
−
2
; ((b))
3
x
4
+
8
x
2
−
3
,
x
3
+
2
x
2
+
3
x
+
6
3x^4 + 8x^2 - 3,\quad x^3 + 2x^2 + 3x + 6
3
x
4
+
8
x
2
−
3
,
x
3
+
2
x
2
+
3
x
+
6
; ((c))
x
4
−
2
x
3
−
2
x
2
−
2
x
−
3
,
x
3
+
6
x
2
+
7
x
+
1
x^4 - 2x^3 - 2x^2 - 2x - 3,\quad x^3 + 6x^2 + 7x + 1
x
4
−
2
x
3
−
2
x
2
−
2
x
−
3
,
x
3
+
6
x
2
+
7
x
+
1
.
Related theory
Greatest Common Divisor And The Euclidean Algorithm
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