Question

如果x3－x2＋x－2＝0,则x^4＋2x3－2x2＋x－1＝_____

Answer 1

x^4＋2x3－2x2＋x－1

=x^4-x^3+x^2-2x+3x^3-3x^2+3x-6+5

=x(x^3-x^2+x-2)+3(x^3-x^2+x-2)+5

∵x^3-x^2+x-2=0

∴原式=5