因式分解：x3-11x2+31x-21

题目

因式分解：x3-11x2+31x-21

答案

x³-11x²+31x-21=(x³-x²)-(10x²-10x)+(21x-21)=x²(x-1)-10x(x-1)+21(x-1)=(x²-10x+21)(x-1)=(x-3)(x-7)(x-1)=(x-1)(x-3)(x-7)