Question

当k=?x^2-xy-6y^2+2x-y+k能分解成两个一次多项式的积

Answer 1

x²-xy-6y²²+2x-y+k

=(x-3y)(x+2y)+2x-y+k

则应等于(x-3y+a)(x+2y+b)

(x-3y+a)(x+2y+b)

=(x-3y)(x+2y)+(a+b)x+(2a-3b)t+ab

=(x-3y)(x+2y)+2x-y+k

所以a+b=2

2a-3b=-1

k=ab

所以a=1,b=1

所以k=ab=1