x³ -5x²+3x+1因式分解x³ -5x²+3x+1

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/05 20:37:48
x³ -5x²+3x+1因式分解x³ -5x²+3x+1

x³ -5x²+3x+1因式分解x³ -5x²+3x+1
x³ -5x²+3x+1因式分解
x³ -5x²+3x+1

x³ -5x²+3x+1因式分解x³ -5x²+3x+1
x³ -5x²+3x+1
=x^3-4x^2+3x-x^2+1
=x(x^2-4x+3)-(x^2-1)
=x(x-1)(x-3)-(x-1)(x+1)
=(x-1)(x^2-4x-1)

解法1
x³ -5x²+3x+1
=x^3-x^2-4x^2+3x+1
=x^2(x-1)-(4x^2-3x-1)
=x^2(x-1)-(x-1)(4x+1)
=(x^2-4x-1)(x-1)
解法2
x³ -5x²+3x+1
=x^3-4x^2+3x-x^2+1
=x(x^2-4x+3)-(x^2-1)
=x(x-1)(x-3)-(x-1)(x+1)
=(x-1)(x^2-4x-1)