因式分解:x^4+x^3-2x^2-x+1
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/04 18:40:50
因式分解:x^4+x^3-2x^2-x+1
![因式分解:x^4+x^3-2x^2-x+1](/uploads/image/z/18317832-24-2.jpg?t=%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%EF%BC%9Ax%5E4%2Bx%5E3-2x%5E2-x%2B1)
x^4+x^3-2x^2-x+1
=(x^4-x^3)+(2x^3-2x^2)-(x-1)
=x^3(x-1)+2x^2(x-1)-(x-1)
=(x-1)(x^3+2x^2-1)
=(x-1)[(x^3+x^2+x^2-1)]
=(x-1)[x^2(x+1)+(x+1)(x-1)]
=(x-1)(x+1)(x^2+x-1) 有理数范围内
=(x-1)(x+1)[x-(√5-1)/2][x+(√5+1)/2] 实数范围内
=(x^4-x^3)+(2x^3-2x^2)-(x-1)
=x^3(x-1)+2x^2(x-1)-(x-1)
=(x-1)(x^3+2x^2-1)
=(x-1)[(x^3+x^2+x^2-1)]
=(x-1)[x^2(x+1)+(x+1)(x-1)]
=(x-1)(x+1)(x^2+x-1) 有理数范围内
=(x-1)(x+1)[x-(√5-1)/2][x+(√5+1)/2] 实数范围内
(x-1)(x-2)(x-3)(x-4)-24 因式分解
(x+1)(x+2)(x+3)(x+4)-24因式分解
因式分解(x+1)(x+2)(x+3)(x+4)-24
因式分解x^4-x^-2-x+1
因式分解:(x^5+x^4+x^3+x^2+x+1)^2-x^5
因式分解(x+1)(x+2)(x+3)(x+4)+x(x+5)
(X+1)(X+2)(X+3)(X+4)+X(X+5) 如何因式分解?
因式分解:4x^3+3x^2+2x+1
因式分解x^4-4x^3+4x^2-1
因式分解(x^2-x)^2-4(x^2-x-1)
x^8+x^6+x^4+x^2+1因式分解
因式分解x^8+x^6+x^4+x^2+1