因式分解:x的4次方+x的3次方-2

题目

因式分解:x的4次方+x的3次方-2

答案

x^4+x^3-2
=x^4-x^3+2x^3-2
=x^3(x-1)+2(x^3-1)
=x^3(x-1)+2(x-1)(x^2+x+1)
=(x-1)[x^3+2(x^2+x+1)]
=(x-1)(x^3+2x^2+2x+2)