Question

已知(x+2y-1) 是二元二次式3x^2+axy+by^2+x+9y-4的一个因式,则a=?b=?

Answer 1

3x^2+axy+by^2+x+9y-4

=(3x^2+6xy-3x)+(a-6)xy+by^2+x+3x+9y-4

=3x(x+2y-1)+(a-6)xy+by^2+(4x+8y-4)+y

=3x(x+2y-1)+(a-6)xy+by^2+4(x+2y-1)+y

=3x(x+2y-1)+4(x+2y-1)+y{(a-6)x+by+1}

所以(a-6)x+by+1是x+2y-1的倍数

所以有a-6=-1,b=-2

a=5,b=-2