2X^3+(2a+23)X^2+(10-7a)X+3a-11分解因式有类似提问,2x^3+(2a+23)x^2+(10-7a)x+3a-11=2x^3-x^2+x^2+(2a+23)x^2+(10-7a)x+3a-11=x^2*(2x-1)+(2a+24)x^2-(a+12)x+(a+12)x+(10-7a)x+3a-11=x^2*(2x-1)+(a+12)x(2x-1)+(22-6a)x-(11-3a)=x^2*(2x-1)+(a+12)x(2x-1)+(1
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![2X^3+(2a+23)X^2+(10-7a)X+3a-11分解因式有类似提问,2x^3+(2a+23)x^2+(10-7a)x+3a-11=2x^3-x^2+x^2+(2a+23)x^2+(10-7a)x+3a-11=x^2*(2x-1)+(2a+24)x^2-(a+12)x+(a+12)x+(10-7a)x+3a-11=x^2*(2x-1)+(a+12)x(2x-1)+(22-6a)x-(11-3a)=x^2*(2x-1)+(a+12)x(2x-1)+(1](/uploads/image/z/2981036-20-6.jpg?t=2X%5E3%2B%282a%2B23%29X%5E2%2B%2810-7a%29X%2B3a-11%E5%88%86%E8%A7%A3%E5%9B%A0%E5%BC%8F%E6%9C%89%E7%B1%BB%E4%BC%BC%E6%8F%90%E9%97%AE%2C2x%5E3%2B%282a%2B23%29x%5E2%2B%2810-7a%29x%2B3a-11%3D2x%5E3-x%5E2%2Bx%5E2%2B%282a%2B23%29x%5E2%2B%2810-7a%29x%2B3a-11%3Dx%5E2%2A%282x-1%29%2B%282a%2B24%29x%5E2-%28a%2B12%29x%2B%28a%2B12%29x%2B%2810-7a%29x%2B3a-11%3Dx%5E2%2A%282x-1%29%2B%28a%2B12%29x%282x-1%29%2B%2822-6a%29x-%2811-3a%29%3Dx%5E2%2A%282x-1%29%2B%28a%2B12%29x%282x-1%29%2B%281)
2X^3+(2a+23)X^2+(10-7a)X+3a-11分解因式有类似提问,2x^3+(2a+23)x^2+(10-7a)x+3a-11=2x^3-x^2+x^2+(2a+23)x^2+(10-7a)x+3a-11=x^2*(2x-1)+(2a+24)x^2-(a+12)x+(a+12)x+(10-7a)x+3a-11=x^2*(2x-1)+(a+12)x(2x-1)+(22-6a)x-(11-3a)=x^2*(2x-1)+(a+12)x(2x-1)+(1
2X^3+(2a+23)X^2+(10-7a)X+3a-11分解因式
有类似提问,
2x^3+(2a+23)x^2+(10-7a)x+3a-11
=2x^3-x^2+x^2+(2a+23)x^2+(10-7a)x+3a-11
=x^2*(2x-1)+(2a+24)x^2-(a+12)x+(a+12)x+(10-7a)x+3a-11
=x^2*(2x-1)+(a+12)x(2x-1)+(22-6a)x-(11-3a)
=x^2*(2x-1)+(a+12)x(2x-1)+(11-3a)(2x-1)
=(2x-1)(x^2+(a+12)+11-3a).但我不知道怎么想上去,
2X^3+(2a+23)X^2+(10-7a)X+3a-11分解因式有类似提问,2x^3+(2a+23)x^2+(10-7a)x+3a-11=2x^3-x^2+x^2+(2a+23)x^2+(10-7a)x+3a-11=x^2*(2x-1)+(2a+24)x^2-(a+12)x+(a+12)x+(10-7a)x+3a-11=x^2*(2x-1)+(a+12)x(2x-1)+(22-6a)x-(11-3a)=x^2*(2x-1)+(a+12)x(2x-1)+(1
如果你不是很理解的话可以用比较传统的方法
先把含有a项与没a项分开得:
原式=(2x^3+(23x^2)+10x-11)+a(2x^2-7x+3)
再进行因式分解会容易很多
接上面:=(2x^3+2x^2+21x^2+10x-11)+
(2ax^-7ax+3a)
=(2x^2(x+1)+(21x-11)(x+1))+a(2x-1)(x-3)=(x+1)(2x^2+21x-11)+a(2x-1)(x-3)
=(x+1)(x+11)(2x-1)+a(2x-1)(x-3)
=(2x-1)((x+1)(x+11)+a(x-3))
=(2x-1)(x^2+(a+12)x+11-3a).
如果你真的想知道,就用3次方程的求根吧
这里著名的有盛金判别法
当然也有3次方程的推导
http://baike.baidu.com/view/460155.htm?fr=ala0_1
这里很详细
当然高中阶段一般是先猜再分解
例如你试探出x=1/2是他的一个根
就可以拆出(2x-1) 再逆推...
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如果你真的想知道,就用3次方程的求根吧
这里著名的有盛金判别法
当然也有3次方程的推导
http://baike.baidu.com/view/460155.htm?fr=ala0_1
这里很详细
当然高中阶段一般是先猜再分解
例如你试探出x=1/2是他的一个根
就可以拆出(2x-1) 再逆推
收起