m2+m+1=0 ,求m3+2m2+2m+3=?

m2+m+1=0 ,求m3+2m2+2m+3=?
m2+m+1=0 ,求m3+2m2+2m+3=?

m2+m+1=0 ,求m3+2m2+2m+3=?
m²+m+1=0 可得：m²+m=-1
原式=m(m²+m)+m²+2m+3
=-m+m²+2m+3
=m²+m+3
=-1+3
=2

m^2+m+1=0
m^3+m^2+m=0
上下两个式子相加
m^3+2m^2+2m+1=0,故而原式=2

m2+m+1=0 ,
m3+2m2+2m+3
=m(m2+m+1)+m2+m+3
=m2+m+3
=m2+m+1+2
=2

m^2+m+1=0
m^3+2m^2+2m+3=m(m^2+m+1+m+1)+3=m(m+1)+3=m^2+m+1+2=2