求m为何值时,多项式x2-y2+mx+5y-6能因式分解,并分解此多项式.
问题描述:
求m为何值时,多项式x2-y2+mx+5y-6能因式分解,并分解此多项式.
答
∵x2-y2=(x+y)(x-y),∴可设x2-y2+mx+5y-6=(x+y+a)(x-y+b).∵(x+y+a)(x-y+b)=x2-xy+bx+xy-y2+by+ax-ay+ab=x2-y2+(a+b)x+(b-a)y+ab,∴x2-y2+mx+5y-6=x2-y2+(a+b)x+(b-a)y+ab.∴a+b=m①b−a=...