因式化简
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/08/23 22:46:39
因式化简
![](http://img.wesiedu.com/upload/1/51/151152987f116dcf717b9b357ff5bfe0.jpg)
![](http://img.wesiedu.com/upload/a/6e/a6e1caab3c832350d1fd53b53e55c901.jpg)
![](http://img.wesiedu.com/upload/1/51/151152987f116dcf717b9b357ff5bfe0.jpg)
![](http://img.wesiedu.com/upload/a/6e/a6e1caab3c832350d1fd53b53e55c901.jpg)
4x^4-4x^3+13x^2-6x+9
=(4x^4-4x^3+x^2)+(12x^2-6x)+9
=(2x^2-x)^2+6(2x²-x)+9
=(2x^2-x+3)^2
=[(2x-3)(x+1)]^2
=(2x-3)^2(x+1)^2
x^4-x^3-7X^2+13x-6
=X^3(x-1)-(7x^2-13x+6)
=x^3(x-1)-(7x-6)(x-1)
=(x-1)(x^3-7x+6)
=(x-1)(x^3-x^2+x^2-x-6x+6)
=(x-1)[x^2(x-1)+ x(x-1)-6(x-1)]
=(x-1)[(x-1)(x^2+x-6)]
=(x-1)^2(x^2+x-6)
=(x-1)^2(x+3)(x-2)
=(4x^4-4x^3+x^2)+(12x^2-6x)+9
=(2x^2-x)^2+6(2x²-x)+9
=(2x^2-x+3)^2
=[(2x-3)(x+1)]^2
=(2x-3)^2(x+1)^2
x^4-x^3-7X^2+13x-6
=X^3(x-1)-(7x^2-13x+6)
=x^3(x-1)-(7x-6)(x-1)
=(x-1)(x^3-7x+6)
=(x-1)(x^3-x^2+x^2-x-6x+6)
=(x-1)[x^2(x-1)+ x(x-1)-6(x-1)]
=(x-1)[(x-1)(x^2+x-6)]
=(x-1)^2(x^2+x-6)
=(x-1)^2(x+3)(x-2)