Question

大学题目f(x)=x^4-4x³+1,与g(x)=x³-3x²+1的最大公因式，求过程

Answer 1

用辗转相除法求两者的最高公因式。下面用分离系数法。
.....................................1..-1
..................------------------------
1 -3 0 1）1 -4 0 0 1
.....................1 -3 0 1
.....................-----------------
............................-1 0 -1 1
............................-1 3 0 -1
............................--------------------
..................................-3 -1 2，

...........................1 -10/3
.............------------------
3 1 -2）3 -9 0 3
................3 1 -2
...............--------------
......................-10 2 3
.....................-10 -10/3 20/3
.....................---------------------
..............................16/3 -11/3，

........................3.....49/16
.............--------------------
16 -11）48 16 -32
................48 -33
..............----------------------
.........................49....-32
.........................49...-539/16
..........................----------------
.................................27/16，
∴f(x)与g(x)的最高公因式是1.