因式分解x^4+1991x^2+1990x+1991
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/03 12:14:31
![因式分解x^4+1991x^2+1990x+1991](/uploads/image/z/1988279-71-9.jpg?t=%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3x%5E4%2B1991x%5E2%2B1990x%2B1991)
因式分解x^4+1991x^2+1990x+1991
因式分解x^4+1991x^2+1990x+1991
因式分解x^4+1991x^2+1990x+1991
答:
x^4+1991x^2+1990x+1991
=(x^4-x)+1991(x^2+x+1)
=x(x^3-1)+1991(x^2+x+1)
=x(x-1)(x^2+x+1)+1991(x^2+x+1)
=(x^2-x+1991)(x^2+x+1)