①由x^2+3x-1=0,得x^2+3x=1
x^3+5x^2+5x+8 =x(x^2+3x)+2x^2+5x+8
=x+2x^2+5x+8
=2(x^2+3x)+8
=2+8
=10
②a^2+b^2-4a+6b+18=(a^2-4a+4)+(b^2+6b+9)+5
=(a-2)*2+(b+3)*2+5
因为(a-2)*2》0,(b+3)*2》0
当a=2,b=-3时,多项式有最小值,最小值为5.