一元三次方程如何因式分解方程1:-x^3+7x^2-16x+12=0是如何变成方程2:-(x-3)(x-2)^2=0求解救!
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/10 21:51:08
![一元三次方程如何因式分解方程1:-x^3+7x^2-16x+12=0是如何变成方程2:-(x-3)(x-2)^2=0求解救!](/uploads/image/z/1962750-30-0.jpg?t=%E4%B8%80%E5%85%83%E4%B8%89%E6%AC%A1%E6%96%B9%E7%A8%8B%E5%A6%82%E4%BD%95%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%E6%96%B9%E7%A8%8B1%EF%BC%9A-x%5E3%2B7x%5E2-16x%2B12%3D0%E6%98%AF%E5%A6%82%E4%BD%95%E5%8F%98%E6%88%90%E6%96%B9%E7%A8%8B2%EF%BC%9A-%28x-3%29%28x-2%29%5E2%3D0%E6%B1%82%E8%A7%A3%E6%95%91%21)
一元三次方程如何因式分解方程1:-x^3+7x^2-16x+12=0是如何变成方程2:-(x-3)(x-2)^2=0求解救!
一元三次方程如何因式分解
方程1:-x^3+7x^2-16x+12=0
是如何变成
方程2:-(x-3)(x-2)^2=0
求解救!
一元三次方程如何因式分解方程1:-x^3+7x^2-16x+12=0是如何变成方程2:-(x-3)(x-2)^2=0求解救!
-x^3+7x^2-16x+12=0
-x³+3x²+(4x²-16x+12)=0
-x²(x-3)+4(x-1)(x-3)=0
(x-3)[-x²+4(x-1)]=0
(x-3)(-x²+4x-4)=0
-(x-3)(x²-4x+4)=0
-(x-3)(x-2)²=0
x³-7x²+16x-12 =x³-3x²-4x²+16x-12
=(x³-3x²)-(4x²-16x+12)
=x²(x-3)-(2x-2)(2x-6)
...
全部展开
x³-7x²+16x-12 =x³-3x²-4x²+16x-12
=(x³-3x²)-(4x²-16x+12)
=x²(x-3)-(2x-2)(2x-6)
=x²(x-3)-4(x-1)(x-3)
=(x-3)(x²-4x+4)
=(x-3)(x-2)²
收起