Question

已知多项式M满足M（y+2）-（y-1）=2y³+3y²+7,试求M

Answer 1

∵最高次是3

则设M=ay^2+by+c

则M(y+2)-(y-1)

=(ay^2+by+c)(y+2)-y+1

=ay^3+2ay^2+by^2+2by+cy+2c-y+1

=ay^3+(2a+b)y^2+(2b+c-1)y+2c+1

=2y^3+3y^2+7

a=2

2a+b=3

b=-1

2b+c-1=0

c=3

所以

M=2y^2-y+3