问题及解答

1.  用 $g(x)$ 除 $f(x)$, 求商 $q(x)$ 与余式 $r(x)$:

(1)  $f(x)=x^3-3x^2-x-1$,  $g(x)=3x^2-2x+1$;

(2)  $f(x)=x^4-2x+5$,  $g(x)=x^2-x+2$.

题目来自 [1] P. 44

References:

[1] 北京大学数学系几何与代数教研室代数小组 编《高等代数》

>> :mode polyn
Switch into polynomial mode.

(1)

>> (x^3-3x^2-x-1)/(3x^2-2x+1)
in> (x^3-3x^2-x-1)/(3x^2-2x+1)

out>
 quotient> q(x) = 1|3x-7|9
remainder> r(x) = -26|9x-2|9

1|3x^1-7|9
------------------------

(2)

in> (x^4-2x+5)/(x^2-x+2)

out> 
 quotient> q(x) = x^2+x-1
remainder> r(x) = -5x+7

x^2+x^1-1
------------------------