1.(x+3)(mx^2+nx-2)
=mx^3+nx^2-2x+3mx^2+3nx-6
=mx^3+(3m+n)x^2+(3n-2)x-6
不含x^2和x项,则其系数为0,
即3m+n=0,3n-2=0
先求出n,再求出m
2.x^2+y^2+2x-4y+7
=x^2+2x+1+y^2-4y+4+2
=(x+1)^2+(y-2)^2+2
根据平方的非负数性质,可知最小值为2,选A
3.x^2+2kx-3k^2能被x-1整除,即含有(x-1)这一因式
分解因式为(x-1)(x+3k^2),展开后为x^2+(3k^2-1)x-3k^2
这与原代数式必须恒等,即2k=3k^2-1,
(3k+1)(k-1)=0,解得k=-1/3或k=1
4.x^2+4x+y^2-6y+13=0,
则x^2+4x+4+y^2-6y+9=0,
即(x+2)^2+(y-3)^2=0
解得x=-2,y=3
再代入求得(x+2y)(x-2y)=-32