整式初一

如果5x^2-kx+7被5x-2除后余6,求k值及商式设5x²-kx+7=(5x-2)(x+b)+6=5x^2+(5b-2)x-2b+6
得:-k=5b-2
6-2b=7
解得:b=-1/2,k=9/2
商式:5x²-9/2x+7=(5x-2)(x-1/2)+6
已知ax^3+bx^2-47x-15可被3x+1和2x-3整除,求a,b
3x-1)(2x-3)=6x^2-11x+3设再乘一个cx+d后等于ax^3+bx^2-47x-15（cx+d）（6x^2-11x+3）=ax^3+bx^2-47x-15 因为3d=-15 所以d=-5（cx-5）（6x^2-11x+3）=6cx^3-(11c+30)x^2+(3c+55)x-15=ax^3+bx^2-47x-15比较系数6c=a -(11c+30)=b +(3c+55)=-47 c=-34 a=-204 b=-404
试求x^285-x^83+x^71+x^9-x^3+x被x-1除,所得的余数
答案:2
因为x^n-1(n≥1)是x-1的倍数,
所以x＾285－x＾83,x＾9－x＾3是x-1的倍数,余下x＾71＋x.
因为x＾71＋x = (x＾71 - 1)＋(x-1) + 2
而x＾71 - 1,x-1是x-1的倍数,所以余数为2
已知x-y=m,y-z=-3,求x^2+y^2+z^2-xy-yz-zx的最小值
设A=x^2+y^2+z^2-xy-yz-zx;
2A=2x^2+2y^2+2z^2-2xy-2yz-2zx;
2A=(x-y)^2+(y-z)^2+(z-x)^2
=m^2+3^2+(m-3)^2
=m^2+9+m^2-6m+9
=2m^2-6m+18
所以A=m^2-6m+9+3m=（m-3)^2+3m
（m-3）最小值为0；所以最小值为3m