Question

分解因式：x^4+x^3+2x^2-x+3

Answer 1

分解不了
原因如下：
x^4+x^3+2x^2-x+3=x^2(x+1/2)^2+3/2x^2+(1/2x-1)^2+2
该式恒大于零
因式分解的条件是x^4+x^3+2x^2-x+3=0有实数解，显然实数解不存在
所以分解不了

Answer 2

答案：x*(x+1)(x^2+1)(x-3)

步骤：x^4+x^2+x^3+ x^2+x-2x+3
=（ x^4+x^2）+（x^3+ x)+(x^2-2x+3)
= x^2(x^2+1) +x(x^2+1)+(x-3)(x+1)
=x*(x+1)(x^2+1)(x-3)

Answer 3

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

Answer 4

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

Answer 5

原式=（x-1）*（x+1）*(x^2+x+3)