若多项式2x^3-kx^2+3被2x+1除后余2.求k

设2x^3-kx^2+3=(2x+1)(x^2+mx+1)+2 2x^3-kx^2+3=2x^3+2mx^2+2x+x^2+mx+1+2 2x^3-kx^2+3=2x^3+(2m+1)x^2+(2+m)x+3 得2m+1=-k 2+m=0所以m=-2 k=3

说明2x^3-kx^2+1 能被2x+1整除2x^3-kx^2+1=(2x+1)(x^2+1-2x)=2x^3-3x^2+1k=3

k=3.2x^3-3x^2+3=(2x+1)(x^2-2x+1)+2