3次方的因式分解的方法 例如X^3 + 2x -3 极限的运用范围..还有给我讲讲泰勒公式

三次方因式分解万能公式:a³+b³=(a+b)(a²-ab+b²)a³-b³ 。把一个多项式在一个范围化为几个整式的积的形式，这种式子变形叫做这个多项式的因式分解。多项式中的每个单项式叫做多项式的项，这些单项式中的最高项次数，就是这个多项式的次数。其中多项式中不含字母的项叫做常数项。数学中用以求解高次一元方程的一种方法。把方程的一侧的数（包括未知数），通过移动使其值化成0，把方程的另一侧各项化成若干因式的乘积，然后分别令各因式等于0而求出其解的方法叫因式分解法。一般的三次方程不能用配方法求解，但四次方程可以。四次方程的标准解法就是引入参数后等式两边配平方，然后两边开方求解，参数通过解一个三次方程得到。得到的四次方程的求根公式里面只有平方根和立方根，没有四次方根，所以通过笔算开平方和开立方，也能直接笔算出四次方程的解。标准型的一元三次方程ax+bx+cx+d=0，解法有：意大利学者卡尔丹1545年发表的卡尔丹公式法。中国学者范盛金于1989年发表的盛金公式法。因式分解法不是对所有的三次方程都适用，只对一些简单的三次方程适用。对于大多数的三次方程，只有先求出它的根，才能做因式分解。对一些简单的三次方程能用因式分解求解的，用因式分解法求解很方便，直接把三次方程降次。

10x³-5x²-5x+3=(x-x1)(x-x2)(x-x3)步骤如下：(1)用十字相乘法分解二次项(得到一个十字相乘图(有两列)。(2)把常数项f分解成两个因式填在第三列上，要求第二、第三列构成的十字交叉之积的和等于原式中，第一、第三列构成的十字交叉之积的和等于原式中的dx。x1=[5-5(³√35)-³√1225]/30 x2=[10+5(³√35)+³√1225]/60+i·√3·[5(³√35)-³√1225]/60 x3=[10+5(³√35)+³√1225]/60-i·√3·[5(³√35)-³√1225]/60 (3)先以一个字母的一次系数分数常数项。(4)再按另一个字母的一次系数进行检验。(5)横向相加，纵向相乘。扩展资料：分解方法因式分解主要有十字相乘法，待定系数法，双十字相乘法，对称多项式，轮换对称多项式法，余式定理法等方法，求根公因式分解没有普遍适用的方法，初中数学教材中主要介绍了提公因式法、运用公式法、分组分解法。而在竞赛上，又有拆项和添减项法式法，换元法，长除法，短除法，除法等。提公因式法如果一个多项式的各项有公因式，可以把这个公因式提出来，从而将多项式化成两个因式乘积的形式，这种分解因式的方法叫做提公因式法。各项都含有的公共的因式叫做这个多项式各项的公因式。公因式可以是单项式，也可以是多项式。具体方法：在确定公因式前，应从系数和因式两个方面考虑。当各项系数都是整数时，公因式的系数应取各项系数的最大公约数字母取各项的相同的字母，而且各字母的指数取次数最低的。当各项的系数有分数时，公因式系数为各分数的最大公约数。如果多项式的第一项为负，要提出负号，使括号内的第一项的系数成为正数。提出负号时，多项式的各项都要变号。

可以尝试用待定系数法进行因式分解，比如ax³+bx²+cx+d＝a(x+e)(x²+fx+g)，拆开计算出e，f，g的值，x²+fx+g能分解则继续分解，不能分解则因式分解完毕。分解一般步骤1、如果多项式的首项为负，应先提取负号；这里的“负”，指“负号”。如果多项式的第一项是负的，一般要提出负号，使括号内第一项系数是正的。2、如果多项式的各项含有公因式，那么先提取这个公因式，再进一步分解因式；要注意：多项式的某个整项是公因式时，先提出这个公因式后，括号内切勿漏掉1；提公因式要一次性提干净，并使每一个括号内的多项式都不能再分解。3、如果各项没有公因式，那么可尝试运用公式、十字相乘法来分解；4、如果用上述方法不能分解，再尝试用分组、拆项、补项法来分解。扩展资料因式分解与解高次方程有密切的关系。对于一元一次方程和一元二次方程，初中已有相对固定和容易的方法。在数学上可以证明，对于一元三次方程和一元四次方程，也有固定的公式可以求解。只是因为公式过于复杂，在非专业领域没有介绍。对于分解因式，三次多项式和四次多项式也有固定的分解方法，只是比较复杂。对于五次以上的一般多项式，已经证明不能找到固定的因式分解法，五次以上的一元方程也没有固定解法。

三次方程因式分解是对一元三次方程的因式分解。例如：解方程x^3-x=0。对左边作因式分解，得x(x+1)(x-1)=0，得方程的三个根：x1=0；x2=1；x3=-1。注意：因式分解方法灵活，技巧性强。学习这些方法与技巧，不仅是掌握因式分解内容所需的，而且对于培养解题技能、发展思维能力都有着十分独特的作用。学习它，既可以复习整式的四则运算，又为学习分式打好基础；学好它，既可以培养学生的观察、思维发展性、运算能力，又可以提高综合分析和解决问题的能力。三次方程简介：三次方程的英文名是Cubic equation，指的是一种数学的方程式。三次方程是未知项总次数最高为3的整式方程。三次方程的解法思想是通过配方和换元，使三次方程降次为二次方程，进而求解。其他解法还有因式分解法、另一种换元法、盛金公式解题法等。

公式法有两个公式：立方和公式：a^3+b^3=(a+b) (a^2-ab+b^2）立方差公式：a^3-b^3=(a-b) (a^2+ab+b^2）分组分解比如：X^3-2X^2+X-2=(X^3-2X^2)+(X-2)=X^2(X-2)+(X-2)=(X^2-2)(X-2)=(X+√2)(X+√2)(X-2)分解一般步骤1、如果多项式的首项为负，应先提取负号；这里的“负”，指“负号”。如果多项式的第一项是负的，一般要提出负号，使括号内第一项系数是正的。2、如果多项式的各项含有公因式，那么先提取这个公因式，再进一步分解因式；要注意：多项式的某个整项是公因式时，先提出这个公因式后，括号内切勿漏掉1；提公因式要一次性提干净，并使每一个括号内的多项式都不能再分解。3、如果各项没有公因式，那么可尝试运用公式、十字相乘法来分解；4、如果用上述方法不能分解，再尝试用分组、拆项、补项法来分解。

1、提公因式法： 果多项式各项都有公共因式，则可先考虑把公因式提出来，进行因式分解，注意要每项都必须有公因式。2、公式法: 即多项式如果满足特殊公式的结构特征，即可采用套公式法，进行多项式的因式分解。3、分组分解法：当多项式的项数较多时，可将多项式进行合理分组，达到顺利分解的目的。当然可能要综合其他分法，且分组方法也不一定唯一。4、换元法:即引入新的字母变量，将原式中的字母变量换掉化简式子。运用此种方法对于某些特殊的多项式因式分解可以起到简化的效果。

设方程为（x+a）*（x+b）*（x+c）=0 展开为X3+（a+b+c）X2+（ab+ac+bc）X+abc=0 和原方程系数比较 X3 X2 X和常数项系数分别相等 求出a b c即可

因式分解法：因式分解法不是对所有的三次方程都适用，只对一些三次方程适用．对于大多数的三次方程，只有先求出它的根，才能作因式分解．当然，因式分解的解法很简便，直接把三次方程降次，例如：解方程x3-x=0对左边作因式分解，得x(x+1)(x-1)=0，得方程的三个根：x1=0,x2=1,x3=-1。另一种换元法：对于一般形式的三次方程，先用上文中提到的配方和换元，将方程化为x3+px+q=0的特殊型．令x=z-p/3z代入并化简，得：z-p/27z+q=0。再令z=w代入，得：w+p/27w+q=0．这实际上是关于w的二次方程．解出w,再顺次解出z,x。扩展资料：盛金公式解法三次方程应用广泛。用根号解一元三次方程，虽然有著名的卡尔丹公式，并有相应的判别法，但使用卡尔丹公式解题比较复杂，缺乏直观性。范盛金推导出一套直接用a、b、c、d表达的较简明形式的一元三次方程的一般式新求根公式，并建立了新判别法。参考资料：三次方程--百度百科

用综合除法

三次因式分解，可以假设有原式=d*(x-a)*(x-b)*(x-c)，然后展开，一一对应x系数得出a,c,b,d，再代回，原式=d*(x-a)*(x-b)*(x-c)，即因式分解

有公式的，以前的教科书有，现在删减掉了，原因是为了减缓学生的压力。这里我就给两道：x^3+y^3=(x+y)(x^2-xy+x^2),x^3-y^3=(x^2-xy+y^2)

一般采用试根法, 基于一个代数理论, 若将实数a代入多项式, 多项式的值为0 则x-a是多项式的一个因式.

a^3-b^3 =（a-b）（a²+ab+b²） a^3+b^3 =（a+b）（a²-ab+b²）这两个是立方差与立方和公式需要你去记住哦

一元三次方程的求根公式用通常的演绎思维是作不出来的，用类似解一元二次方程的求根公式的配方法只能将型如ax^3+bx^2+cx+d+0的标准型一元三次方程形式化为x^3+px+q=0的特殊型。 一元三次方程的求解公式的解法只能用归纳思维得到，即根据一元一次方程、一元二次方程及特殊的高次方程的求根公式的形式归纳出一元三次方程的求根公式的形式。归纳出来的形如 x^3+px+q=0的一元三次方程的求根公式的形式应该为x=A^(1/3)+B^(1/3)型，即为两个开立方之和。归纳出了一元三次方程求根公式的形式，下一步的工作就是求出开立方里面的内容，也就是用p和q表示A和B。方法如下： （1）将x=A^(1/3)+B^(1/3)两边同时立方可以得到 （2）x^3=(A+B)+3(AB)^(1/3)(A^(1/3)+B^(1/3)) （3）由于x=A^(1/3)+B^(1/3)，所以（2）可化为 x^3=(A+B)+3(AB)^(1/3)x，移项可得 （4）x^3－3(AB)^(1/3)x－(A+B)＝0，和一元三次方程和特殊型x^3+px+q=0作比较，可知 （5）－3(AB）^（1/3）＝p,－(A+B)=q，化简得 （6）A+B＝－q，AB＝-（p/3）^3 （7）这样其实就将一元三次方程的求根公式化为了一元二次方程的求根公式问题，因为A和B可以看作是一元二次方程的两个根，而(6)则是关于形如ay^2+by+c=0的一元二次方程两个根的韦达定理，即 （8）y1＋y2＝－（b/a）,y1*y2=c/a (9)对比（6）和（8），可令A＝y1，B＝y2，q＝b/a，-（p/3）^3＝c/a (10)由于型为ay^2+by+c=0的一元二次方程求根公式为 y1＝－（b＋（b^2－4ac）^(1/2)）/(2a) y2＝－（b－（b^2－4ac）^(1/2)）/(2a) 可化为 (11)y1＝－(b/2a)-((b/2a)^2-(c/a))^(1/2) y2＝－(b/2a)+((b/2a)^2-(c/a))^(1/2) 将(9)中的A＝y1，B＝y2，q＝b/a，-（p/3）^3＝c/a代入（11）可得 (12)A＝－(q/2)-((q/2)^2＋（p/3）^3）^(1/2) B＝－(q/2)+((q/2)^2＋（p/3）^3）^(1/2) (13)将A，B代入x=A^(1/3)+B^(1/3)得 (14)x=（－(q/2)-((q/2)^2＋（p/3）^3）^(1/2)）^(1/3)+（－(q/2)+((q/2)^2＋（p/3）^3）^(1/2)）^(1/3) 式 (14)只是一元三方程的一个实根解，按韦达定理一元三次方程应该有三个根，不过按韦达定理一元三次方程只要求出了其中一个根，另两个根就容易求出了

(a-b)的三次方：a^3-3a^2b+3ab^2-b^3(a+b)的三次方：a^3+3a^2b+3ab^2+b^3三次方因式分解：设方程为（x+a）*（x+b）*（x+c）=0，展开为X3+（a+b+c）X2+（ab+ac+bc）X+abc=0和原方程系数比较 X3 X2 X和常数项系数分别相等 求出a b c即可1、如果多项式的首项为负，应先提取负号；这里的“负”，指“负号”。如果多项式的第一项是负的，一般要提出负号，使括号内第一项系数是正的。2、如果多项式的各项含有公因式，那么先提取这个公因式，再进一步分解因式；要注意：多项式的某个整项是公因式时，先提出这个公因式后，括号内切勿漏掉1；提公因式要一次性提干净，并使每一个括号内的多项式都不能再分解。3、如果各项没有公因式，那么可尝试运用公式、十字相乘法来分解；4、如果用上述方法不能分解，再尝试用分组、拆项、补项法来分解。口诀：先提首项负号，再看有无公因式，后看能否套公式，十字相乘试一试，分组分解要合适。

(a-b)的三次方：a^3-3a^2b+3ab^2-b^3(a+b)的三次方：a^3+3a^2b+3ab^2+b^3三次方因式分解：设方程为（x+a）*（x+b）*（x+c）=0，展开为X3+（a+b+c）X2+（ab+ac+bc）X+abc=0和原方程系数比较 X3 X2 X和常数项系数分别相等 求出a b c即可1、如果多项式的首项为负，应先提取负号；这里的“负”，指“负号”。如果多项式的第一项是负的，一般要提出负号，使括号内第一项系数是正的。2、如果多项式的各项含有公因式，那么先提取这个公因式，再进一步分解因式；要注意：多项式的某个整项是公因式时，先提出这个公因式后，括号内切勿漏掉1；提公因式要一次性提干净，并使每一个括号内的多项式都不能再分解。3、如果各项没有公因式，那么可尝试运用公式、十字相乘法来分解；4、如果用上述方法不能分解，再尝试用分组、拆项、补项法来分解。口诀：先提首项负号，再看有无公因式，后看能否套公式，十字相乘试一试，分组分解要合适。

x的三次方加一的因式分解：x³+1=（x+1）（x²-x+1）x³-1=（x-1）（x²+x+1）。三次方因式分解法很简便，直接把三次方程降次，例如：解方程x3-x=0，对左边作因式分解，得x(x+1)(x-1)=0，得方程的三个根：x1=0,x2=1,x3=-1。三次方怎么因式分解：设方程为（x+a）*（x+b）*（x+c）=0展开为X3+（a+b+c）X2+（ab+ac+bc）X+abc=0和原方程系数比较X3，X2，X和常数项系数分别相等，求出a，b，c即可。如果多项式的首项为负，应先提取负号；这里的“负”，指“负号”。如果多项式的第一项是负的，一般要提出负号，使括号内第一项系数是正的。把一个多项式化为几个最简整式的乘积的形式，这种变形叫做把这个多项式因式分解。它是中学数学中最重要的恒等变形之一，它被广泛地应用于初等数学之中，是我们解决许多数学问题的有力工具。因式分解方法灵活，技巧性强，学习这些方法与技巧，不仅是掌握因式分解内容所必需的。而且对于培养学生的解题技能，发展学生的思维能力，都有着十分独特的作用。学习它，既可以复习整式的四则运算，又为学习分式打好基础；学好它，既可以培养学生的观察、思维发展性、运算能力，又可以提高学生综合分析和解决问题的能力。因式分解的原则：1、分解因式是多项式的恒等变形，要求等式左边必须是多项式。2、分解因式的结果必须是以乘积的形式表示。3、每个因式必须是整式，且每个因式的次数都必须低于原来多项式的次数。

(a+b)3=a3+b3+3ab2+3a2b

讲因式分解必须某个数域内讨论。如果在复数域内讨论，那一元3次多项式肯定可以分解。

三次方因式分解公式：a³+b³=（a+b）（a²-ab+b²）a³-b³。把一个多项式在一个范围（如实数范围内分解，即所有项均为实数）化为几个整式的积的形式，这种式子变形叫做这个多项式的因式分解，也叫作把这个多项式分解因式。在数学中，由若干个单项式相加组成的代数式叫做多项式（若有减法：减一个数等于加上它的相反数）。多项式中的每个单项式叫做多项式的项，这些单项式中的最高项次数，就是这个多项式的次数。其中多项式中不含字母的项叫做常数项。

a^3-3a+2=a^3-a-2a+2=a(a*a-1)-2*(a-1)=(a-1)(a*(a+1)-2)=(a-1)(a+2)(a-1)

要牢记立方和、立方差公式：a³+b³=（a+b）（a²-ab+b²）a³-b³= （a-b）（a²+ab+b²）

一般来说三次方程都可以分解为以下几种形式：原式=（x+a）（x+b）（x+c）或 （ax^2+bx+c）(x+d)或（x^2+bx+c）(ax+d)然后根据各项系数 和abcd的对应关系就可以求出系数了一般第一种比较常用只要记住这一点，分解3次方程就不会很难了

先提公共的因式，再像二次那样因式分解。因式分解的步骤：1、提取公因式这个是最基本的，就是有公因式就提出来（相同取出来剩下的相加或相减）。2、完全平方看到式字内有两个数平方就要注意下了，找找有没有两数积的两倍，有的话就按照公式进行。3、平方差公式这个要熟记，因为在配完全平方时有可能会拆添项，如果前面是完全平方，后面又减一个数的话，就可以用平方差公式再进行分解。4、十字相乘首先观察，有二次项，一次项和常数项，可以采用十字相乘法，（十字相乘法的方法：十字左边相乘等于二次项系数，右边相乘等于常数项，交叉相乘再相加等于一次项系数）。三次函数性态的五个要点1、三次函数y=f(x）在（－∞，＋∞）上的极值点的个数。2、三次函数y=f（x）的图象与x轴交点个数。3、单调性问题。4、三次函数f（x）图象的切线条数。5、融合三次函数和不等式，创设情境求参数的范围。

一般使用 X 3 -y 3 =(x+y)(x 2 -xy+y 2 ) X 3 +y 3 =(x-y)(x 2 +xy+y 2 ) (x+y) 3 = X 3 +3x 2 y+3xy 2 +y 3 (x-y) 3 = X 3 -3x 2 y+3xy 2 -y 3 四个公式

（x-1)(x-4)(x+2)

1.因式分解法因式分解法不是对所有的三次方程都适用，只对一些三次方程适用．对于大多数的三次方程，只有先求出它的根，才能作因式分解．当然，因式分解的解法很简便，直接把三次方程降次．例如：解方程x^3-x=0 对左边作因式分解，得x(x+1)(x-1)=0,得方程的三个根：x1=0,x2=1,x3=-1.2.另一种换元法对于一般形式的三次方程，先用上文中提到的配方和换元，将方程化为x+px+q=0的特殊型．令x=z-p/3z,代入并化简，得：z-p/27z+q=0.再令z=w,代入，得：w+p/27w+q=0．这实际上是关于w的二次方程．解出w,再顺次解出z,x.3.盛金公式解题法三次方程应用广泛。用根号解一元三次方程，虽然有著名的卡尔丹公式，并有相应的判别法，但使用卡尔丹公式解题比较复杂，缺乏直观性。范盛金推导出一套直接用a、b、c、d表达的较简明形式的一元三次方程的一般式新求根公式，并建立了新判别法．盛金公式一元三次方程aX^3＋bX^2＋cX＋d=0，（a，b，c，d∈R，且a≠0）。 重根判别式：A=b^2－3ac；B=bc－9ad；C=c^2－3bd， 总判别式：Δ=B^2－4AC。 当A=B=0时，盛金公式①： X1=X2=X3=－b/(3a)=－c/b=－3d/c。 当Δ=B^2－4AC>0时，盛金公式②： X1=(－b－(Y1)^(1/3)－(Y2)^(1/3))/(3a)； X2，3=(－2b＋(Y1)^(1/3)＋(Y2)^(1/3))/(6a)±i3^(1/2)((Y1)^(1/3)－(Y2)^(1/3))/(6a)， 其中Y1，2=Ab＋3a(－B±(B^2－4AC)^(1/2))/2，i^2=－1。 当Δ=B^2－4AC=0时，盛金公式③： X1=－b/a＋K； X2=X3=－K/2， 其中K=B/A，(A≠0)。 当Δ=B^2－4AC<0时，盛金公式④： X1=(－b－2A^(1/2)cos(θ/3))/(3a)； X2，3=(－b＋A^(1/2)(cos(θ/3)±3^(1/2)sin(θ/3)))/(3a)， 其中θ=arccosT，T=(2Ab－3aB)/(2A^(3/2))，(A>0，－1<T<1)。盛金判别法①：当A=B=0时，方程有一个三重实根； ②：当Δ=B^2－4AC>0时，方程有一个实根和一对共轭虚根； ③：当Δ=B^2－4AC=0时，方程有三个实根，其中有一个两重根； ④：当Δ=B^2－4AC<0时，方程有三个不相等的实根。盛金定理当b=0，c=0时，盛金公式①无意义；当A=0时，盛金公式③无意义；当A≤0时，盛金公式④无意义；当T＜-1或T＞1时，盛金公式④无意义。 当b=0，c=0时，盛金公式①是否成立？盛金公式③与盛金公式④是否存在A≤0的值？盛金公式④是否存在T＜-1或T＞1的值？盛金定理给出如下回答： 盛金定理1：当A=B=0时，若b=0，则必定有c=d=0（此时，方程有一个三重实根0，盛金公式①仍成立）。 盛金定理2：当A=B=0时，若b≠0，则必定有c≠0（此时,适用盛金公式①解题）。 盛金定理3：当A=B=0时，则必定有C=0（此时,适用盛金公式①解题）。 盛金定理4：当A=0时，若B≠0，则必定有Δ＞0（此时，适用盛金公式②解题）。 盛金定理5：当A＜0时，则必定有Δ＞0（此时，适用盛金公式②解题）。 盛金定理6：当Δ=0时，若B=0，则必定有A=0（此时，适用盛金公式①解题）。 盛金定理7：当Δ=0时，若B≠0，盛金公式③一定不存在A≤0的值（此时，适用盛金公式③解题）。 盛金定理8：当Δ＜0时，盛金公式④一定不存在A≤0的值。（此时，适用盛金公式④解题）。 盛金定理9：当Δ＜0时，盛金公式④一定不存在T≤-1或T≥1的值，即T出现的值必定是-1＜T＜1。 显然，当A≤0时，都有相应的盛金公式解题。 注意：盛金定理逆之不一定成立。如：当Δ＞0时，不一定有A＜0。 盛金定理表明：盛金公式始终保持有意义。任意实系数的一元三次方程都可以运用盛金公式直观求解。 当Δ=0(d≠0)时，使用卡尔丹公式解题仍存在开立方。与卡尔丹公式相比较，盛金公式的表达形式较简明，使用盛金公式解题较直观、效率较高；盛金判别法判别方程的解较直观。重根判别式A=b^2－3ac；B=bc－9ad；C=c^2－3bd是最简明的式子，由A、B、C构成的总判别式Δ=B^2－4AC也是最简明的式子（是非常美妙的式子），其形状与一元二次方程的根的判别式相同；盛金公式②中的式子(－B±(B^2－4AC)^(1/2))/2具有一元二次方程求根公式的形式，这些表达形式体现了数学的有序、对称、和谐与简洁美。盛金公式出处以上盛金公式的结论，发表在《海南师范学院学报（自然科学版）》（第2卷，第2期；1989年12月，中国海南。国内统一刊号：CN46-1014），第91―98页。范盛金，一元三次方程的新求根公式与新判别法。

解原式=a(3a²-2a+1) =a(a-1)(3a+1) 原式= -2p(3p²+5p-1) 在用公式法

=a^3+a^2-(a^2+3a+2)=a^2(a+1)-(a+1)(a+2)=(a+1)(a^2-a-2)=(a+1)(a+1)(a-2)=...

无论是一元几次多项式的因式分解，一般只要出题要你因式分解，一般都可以分解。1）公式法：主要看未知数的系数是否可以套用公式：比如完全立方公式x^3+3ax^2+3a^2x+a^3=（x+a）^3,和x^3-3ax^2+3a^2x-a^3=（x-a）^3；还有公式：x^3-a^3=(x-a)(x^2+ax+a^2);当然，一般增加难度时，打乱排列的顺序，增加个公共系数另外加个常数项负1，例如对：8x^3+24x^2+24x+7的因式分解。整个式子表面看没有公因式，就需要你动手变形，变为：8x^3+24x^2+24x+7+1-1=8*(x^3+3x^2+3x+1)-1=8*(x+1)^3-1=[2(x+1)]^3-1=[2(x+1)-1]*{[2(x+1)]^2+2(x+1)+1}=(2x+1)(4x^2+8x+4+2x+2+1)=(2x-1)(4x^2+10x+7)。2）降幂法：看提取一元公因式后，是否可以变为二次方程的应用公式：完全平方公式和二数和乘以二数差等于二数平方差。3）组合法：不能利用公式的，可以两两组合，看是否有公因式，如果有公因式，分别提取公因式，进行因式分解。4）拆分法：一般一元三次方程在没有其它代数的情况下是四个项，有时为了因式分解，要把四项变为六项，看两两组合是否有公因式可以提取，再因式分解。因式分解题型很多，不是我靠三言两语就能说清楚的，你必须多做题，题做的多了，你自然就会了；你会比我总结的还要好。

一元三次方程的标准形是ax^3+bx^2+cx+d=0。三次方程的解法思想是通过配方和换元，使三次方程降次为二次方程，进而求解。其他解法还有因式分解法、另一种换元法、盛金公式解题法等。注：三次方程至少有一个实数根，但形式可能比较复杂。

公式法，也是最简单的。不过有时候不容易看出来  需要整体的思想。分组分解法：合理的分组再提取公因式求根法：令多项式等于零，带入数值a看看是否成立，若成立，则x-a必然是其中一个因式，然后在配凑  转化成二次方的因式分解。       数值a的选取：a一定是常数项的约数 并且一般来说都是一些简单的数字

x³-3x²+4=(x³+x²)-4（x²-1）=x²（x+1）-4（x+1)(x-1)=(x+1)(x²-4x+4)=(x+1）（x-2)²ab(c²-d²)+cd(a²-b²)=abc²-abd²+cda²-cdb²=abc²+cda²-(abd²+cdb²)=ac(bc+ad)-bd(ad+bc)=(ad+bc)(ac-bd)x²-4mx+8mn-4n⁴=x⁴+64=x³-11x²+31x-21=x³-4xy²-2x²y+8y³=

(x-2)(-x^2-x+6)=0(x-2)(x-2)(-3-x)=0(-3-x)(x-2)^2=0

（a+b）（a^2-ab+b^2）

三次方因式分解公式：a³+b³=（a+b）（a²-ab+b²）a³-b³。把一个多项式在一个范围（如实数范围内分解，即所有项均为实数）化为几个整式的积的形式，这种式子变形叫做这个多项式的因式分解，也叫作把这个多项式分解因式。在数学中，由若干个单项式相加组成的代数式叫做多项式（若有减法：减一个数等于加上它的相反数）。多项式中的每个单项式叫做多项式的项，这些单项式中的最高项次数，就是这个多项式的次数。其中多项式中不含字母的项叫做常数项。因式分解法：因式分解法不是对所有的三次方程都适用,只对一些三次方程适用。对于大多数的三次方程,只有先求出它的根,才能作因式分解。当然,因式分解的解法很简便,直接把三次方程降次。例如：解方程x^3-x=0 对左边作因式分解,得x(x+1)(x-1)=0,得方程的三个根：x1=0,x2=1,x3=-1。另一种换元法：对于一般形式的三次方程,先用上文中提到的配方和换元,将方程化为x+px+q=0的特殊型。令x=z-p/3z,代入并化简，得：z-p/27z+q=0.再令z=w,代入,得：w+p/27w+q=0。这实际上是关于w的二次方程．解出w,再顺次解出z,x。盛金公式解题法：三次方程应用广泛，用根号解一元三次方程,虽然有著名的卡尔丹公式,并有相应的判别法,但使用卡尔丹公式解题比较复杂,缺乏直观性。范盛金推导出一套直接用a、b、c、d表达的较简明形式的一元三次方程的一般式新求根公式,并建立了新判别法。盛金公式：一元三次方程aX^3＋bX^2＋cX＋d=0,（a,b,c,d∈R,且a≠0）。重根判别式：A=b^2－3ac；B=bc－9ad；C=c^2－3bd,总判别式：Δ=B^2－4AC.当A=B=0时,盛金公式：X1=X2=X3=－b/(3a)=－c/b=－3d/c。当Δ=B^2－4AC>0时,盛金公式：X1=(－b－(Y1)^(1/3)－(Y2)^(1/3))/(3a)。 X2,3=(－2b＋(Y1)^(1/3)＋(Y2)^(1/3))/(6a)±i3^(1/2)((Y1)^(1/3)－(Y2)^(1/3))/(6a),其中Y1,2=Ab＋3a(－B±(B^2－4AC)^(1/2))/2,i^2=－1。当Δ=B^2－4AC=0时,盛金公式③：X1=－b/a＋K； X2=X3=－K/2,其中K=B/A,(A≠0).当Δ=B^2－4AC0,－1。

还是我来回答吧目前公式极其复杂，所以只能猜根有一个根，就有一个因式（x-根）然后剩下二次式，可以分解了给个最佳吧。。。挺难吗？

可以的 x³-1-3x+3=0 (x-1)(x²+x+1)-3(x-1)=0 (x-1)(x²+x-2)=0 (x-1)²(x+2)=0 x=1,x=-2

试根法公式法分组法

先提出一个x，再对括号里的因式分解，如果不可以就提出部分括号里的常数，但要注意乘x。再对后面的进行因式分解，最后整体进行因式分解，有化简的可以继续进行，最后完全分解

先提出一个x，再对括号里的因式分解，如果不可以就提出部分括号里的常数，但要注意乘x。再对后面的进行因式分解，最后整体进行因式分解，有化简的可以继续进行，最后完全分解

20x^3-6x^2-3x-4=20x^3-16x^2+10x^2-8x+5x-4=4x^2(5x-4)+2x(5x-4)+(5x-4)=(5x-4)(4x^2+2x+1).

例如：x3 + 3x2 - 6x - 18x3 + 3x2 - 6x - 18=x2(x+3) -6(x+3)=(x2-6)(x+3)

ax³+bx²+cx+d=0

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The best hotel to opt for your stay here would be the Peninsula since it is very close to the major attractions in New York and shopping malls and museums too are easily accessible. Vienna:One of the major cities located in Austria this is one place that mingles together in ethnicity, style and sophistication. The city is sure to bring a lasting impression to anyone who pays a visit the very first time. With numerous churches and museums your trip to this fantastic city is sure to be amazing. Besides these if you want to spend an evening in tranquility then the parks are the best places you must visit. The city hall park is a famous and massive park that has a wonderful decoration that is worthwhile. The central tower is the most outstanding feature of the park. The city also has famous restaurants for a comfortable stay. Have a fun filled time in this romantic city. New Orleans:The city of New Orleans is famous for its colors and festivities. 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There are the beaches that are sure to bring you into the most romantic mood. So have a fantastic time here. Melbourne:The second largest city in Australia, Melbourne has a large number of shopping malls that enable you to purchase the perfect gift for your loved one. Besides malls the romantic city also has boutiques that offer a wide variety of daily use articles and trendy clothes and other things. The art and architecture are a major attraction. Well known for its sporting events the city also has people who are often a part of the various festivities that take place in the city. The Australian football league a well-known event is often staged in this beautiful city. The rising and setting sun can be captured in your cameras. So don"t miss out on this romantic city on your visit to Australia and have a fabulous time.

　外貌描写的句子如下：1、她的头发很浓密，而且好像马鬃毛一样的粗硬。却带着小孩子一样的骚乱和柔美，卷曲地绕着她的小小的耳朵。2、她的黑发像轻纱一样垂在肩上。3、浓眉下面深藏着一对炯灼的眼睛，那里面饱含着无边的慈爱。4、她的头发颜色漆黑，带有反光，像乌鸦的翅膀一样，又黑又亮。5、小女儿真像一株海棠似的袅娜。6、眉不太宽厚却浓密真切，横横的两条，永远像新经剔拔过或描画过。7、他的脚趾头差不多同手指头一样长，一样灵活，他能够用脚趾头夹着一支钢笔流利地签名，还能用脚趾头剥豌豆。8、他的脸盘不大，瘦削而有雀斑，下巴尖尖的，像松鼠一样。9、他的一双手很大，骨节突出，颜色发达。手掌上全是茧子，看上去好像被铁锈分成一条条似的。10、她娇艳的脸上有一层新鲜的绒毛，如刚摘下的水蜜桃一样。11、他的红的近乎赭色的脸像是用泥士塑成的，又像是在窑里边被烧炼过，显得结实，坚硬。12、纳赛尔是个高大而坚实的人，很容易使人联想到埃及遍野的椰枣树，挺得住暴风雨的。13、风磨前站着一个矮个的、整个身子活像用铅捶成的人。14、他的脸红彤彤的。瘦瘦的。活像一块风干了的老木头。15、她那黑亮黑亮的头发像柳丝一样轻柔。16、他浅眉细眼，白净的小圆脸。常带着一对生动的笑窝儿。是个模样挺招人喜欢的孩子。17、他的头发和平时一样，乱得像一把破笤帚。18、眉毛高高在上，跟眼睛远隔得彼此要害相思病。19、他把两条愁云紧锁的灰色眉毛更加紧蹙在眼睛上面，这两条眉毛像繁生的高耸的山岭上的灌木丛，山顶上盖满了银针一般的北国寒霜。20、他原来有些弯曲的背，现在越驼越厉害，如同背着一口锅。21、背上那条黑长的大辫子，沉甸甸的，巴掌宽的红辫根儿，远远看去，好像茂林中的一团野火。22、她脱下帽子，比丝更细更软的淡黄色的头发，照着树隙中透下来的阳光，像黄金一般闪耀。23、她那道浓厚而且长得异样的花白眉毛，是卷起的和倒立的，筒直像是两撇搁错了位置的髭须。24、爷爷就像一棵给河浪卷来扔到这儿沙滩上的干桔老树。25、她那柔软好看的脚上穿着足踝处绣着灰蓝色花朵的纱袜，一只脚正在轻轻地拍着地面，好像故意要展露她那丰满匀称的小腿似的。

切字多音字组词：亲切、切记、切身、密切、贴切、急切、真切、殷切、恳切、凄切、余切、一切、切近、迫切、痛切、切实、切割、热切、切磋、切糕、切音、哀切、切中、关切、清切、切脉、切片、切切、切当、悲切、

**HAMLET** 1 [73] This is that Hamlet the Dane whom we read of in our youth, and whom we may be said almost to remember in [74] our after years; he who made that famous soliloquy on life, who gave the advice to the players, who thought "this goodly frame, the earth," a sterile promontory, and "this brave o"er-hanging firmament, the air, this majestical roof fretted with golden fire," "a foul and pestilent congregation of vapours;" whom "man delighted not, nor woman neither;" he who talked with the grave-diggers, and moralised on Yorrick"s skull; the school-fellow of Rosencraus and Guildenstern at Wittenburg; the friend of Horatio; the lover of Ophelia; he that was mad and sent to England; the slow avenger of his father"s death; who lived at the court of Horwendillus five hundred years before we were born, but all whose thoughts we seem to know as well as we do our own, because we have read them in Shakespear. Hamlet is a name; his speeches and sayings but the idle coinage of the poet"s brain. What then, are they not real? They are as real as our own thoughts. Their reality is in the reader"s mind. It is we who are Hamlet. This play has a prophetic truth, which is above that of history. Whoever has become thoughtful and melancholy through his own mishaps or those of others; whoever has borne about with him the clouded brow of reflection, and thought himself "too much i" th" sun;" whoever has seen the golden lamp of day dimmed by envious mists rising in his own breast, and could find in the world before him only a dull blank with nothing left remarkable in it; whoever has known "the pangs of despised love, the insolence of office, or the spurns which patient merit of the unworthy takes;" he who has felt his mind sink within him, and sadness cling to his heart like a malady, who has had his hopes blighted and his youth staggered by the apparitions of strange things; who cannot well be at ease, while he sees evil hovering near him like a spectre; whose powers of action have been eaten up by thought, he to whom the universe seems infinite, and himself nothing; whose bitterness [75] of soul makes him careless of consequences, and who goes to a play as his best resource is to shove off, to a second remove, the evils of life by a mock representation of them - this is the true Hamlet. We have been so used to this tragedy that we hardly know how to criticise it any more than we should know how to describe our own faces. But we must make such observations as we can. It is the one of Shakespear"s plays that we think of the oftenest, because it abounds most in striking reflections on human life, and because the distresses of Hamlet are transferred, by the turn of his mind, to the general account of humanity. Whatever happens to him we apply to ourselves, because he applies it so himself as a means of general reasoning. He is a great moraliser; and what makes him worth attending to is, that he moralises on his own feelings and experience. He is not a common-place pedant. If "Lear" is distinguished by the greatest depths of passion, "Hamlet" is the most remarkable for the ingenuity, originality, and unstudied development of character. Shakespear had more magnanimity than any other poet, and he has shown more of it in this play than in any other. There is no attempt to force an interest: everything is left for time and circumstances to unfold. The attention is excited without effort, the incidents succeed each other as matters of course, the characters think and speak and act just as they might do if left entirely to themselves. There is no set purpose, no straining at a point. The observations are suggested by the passing scene - the gusts of passion come and go like sounds of music borne on the wind. The whole play is an exact transcript of what might be supposed to have taken place at the court of Denmark, at the remote period of time fixed upon, before the modern refinements in morals and manners were heard of. It would have been interesting enough to have been admitted as a bystander in such a scene, at such a time, to have heard and witnessed [76] something of what was going on. But here we are more than spectators. We have not only "the outward pageants and the signs of grief;" but "we have that within which passes show." We read the thoughts of the heart, we catch the passions living as they rise. Other dramatic writers give us very fine versions and paraphrases of nature; but Shakespear, together with his own comments, gives us the original text, that we may judge for ourselves. This is a very great advantage. The character of Hamlet stands quite by itself. It is not a character marked by strength of will or even of passion, but by refinement of thought and sentiment. Hamlet is as little of the hero as a man can well be : but he is a young and princely novice, full of high enthusiasm and quick sensibility - the sport of circumstances, questioning with fortune and refining on his own feelings, and forced from the natural bias of his disposition by the strangeness of his situation. He seems incapable of deliberate action, and is only hurried into extremities on the spur of the occasion, when he has no time to reflect, as in the scene where he kills Polonius, and again, where he alters the letters which Rosencraus and Guildenstern are taking with them to England, purporting his death. At other times, when he is most bound to act, he remains puzzled, undecided, and sceptical, dallies with his purposes, till the occasion is lost, and finds out some pretence to relapse into indolence and thoughtfulness again. For this reason he refuses to kill the King when he is at his prayers, and by a refinement in malice, which is in truth only an excuse for his own want of resolution, defers his revenge to a more fatal opportunity, when he shall be engaged in some act "that has no relish of salvation in it." "Now might I do it pat now he is praying; And now I"ll do "t; - and so he goes to heaven; And so am I reveng"d? - that would be scanned: A villain kills my father; and for that [77] I, his sole son, do this same villain send To heaven. O, this is hire and salary, not revenge ... Up sword; and know thou a more horrid hent, When he is drunk asleep, or in his rage." 2 He is the prince of philosophical speculators; and because he cannot have his revenge perfect, according to the most refined idea his wish can form, he declines it altogether. So he scruples to trust the suggestions of the ghost, contrives the scene of the play to have surer proof of his uncle"s guilt, and then rests satisfied with this confirmation of his suspicions, and the success of his experiment, instead of acting upon it. Yet he is sensible of his own weakness, taxes himself with it, and tries to reason himself out of it: "How all occasions do inform against me, And spur my dull revenge! What is a man, If his chief good and market of his time Be but to sleep and feed? A beast; no more. Sure he that made us with such a large discourse, Looking before and after, gave us not That capability and god-like reason To fust in us unus"d. Now whether it be Bestial oblivion, or some craven scruple Of thinking too precisely on th" event, - A thought which, quarter"d, hath but one part wisdom, And ever three parts coward, - I do not know Why yet I live to say, This thing"s to do; Sith I have cause, and will, and strength, and means To do "t. Examples, gross as earth, exhort me: Witness this army of such mass and charge, Led by a delicate and tender prince, Whose spirit with divine ambition puff"d, Makes mouths at the invisible event, Exposing what is mortal and unsure To all that fortune, death, and danger dare, Even for an egg-shell. Rightly to be great Is not to stir without great argument; But greatly to find quarrel in a straw, [78] When honour"s at the stake. How stand I, then, That have a father kill"d, a mother stain"d, Excitements of my reason and my blood, And let all sleep? while, to my shame, I see The imminent death of twenty thousand men, That for a fantasy and trick of fame, Go to their graves like beds, fight for a plot Whereon the numbers cannot try the cause, Which is not tomb enough and continent To hide the slain? - O, from this time forth, My thoughts be bloody, or be nothing worth. "3 Still he does nothing; and this very speculation on his own infirmity only affords him another occasion for indulging it. It is not from any want of attachment to his father or of abhorrence of his murder that Hamlet is thus dilatory; but it is more to his taste to indulge his imagination in reflecting upon the enormity of the crime and refining on his schemes of vengeance, than to put them into immediate practice. His ruling passion is to think, not to act: and any vague pretext that flatters this propensity instantly diverts him from his previous purposes. The moral perfection of this character has been called in question, we think, by those who do not understand it. It is more interesting than according to rules; amiable, though not faultless. The ethical delineations of that "noble and liberal casuist" (as Shakespear has been well called) do not exhibit the drab-coloured quakerism of morality. His plays are not copied either from the "Whole Duty of Man," or from "The Academy of Compliments!" 4 We confess we are a little shocked at the want of refinement in Hamlet. The neglect of punctilious exactness in his behaviour either partakes of the "licence of the time," or else belongs to the very excess of intellectual [79] refinement in the character, which makes the common rules of life, as well as his own purposes, sit loose upon him. He may be said to be amenable only to the tribunal of his own thoughts, and is too much taken up with the airy world of contemplation to lay as much stress as he ought on the practical consequences of things. His habitual principles of action are unhinged and out of joint with the time. His conduct to Ophelia is quite natural in the circumstances. It is that of assumed severity only. It is the effect of disappointed hope, of bitter regrets, of affections suspended, not obliterated, by the distractions of the scene around him! Amidst the natural and preternatural horrors of his situation, he might be excused in delicacy from carrying on his regular courtship. When "his father"s spirit was in arms," it was not a time for the son to make love in. He could neither marry Ophelia, nor wound her mind by explaining the cause of his alienation, which he durst hardly trust himself to think of. It would have taken him years to have come to a direct explanation on the point. In the harassed state of his mind, he could not have done much otherwise than he did. His conduct does not contradict what he says when he sees her funeral, "I loved Ophelia: forty thousand brothers Could not with all their quantity of love Make up my sum" - 5 Nothing can be more affecting or beautiful than the Queen"s apostrophe to Ophelia on throwing flowers into the grave. "Sweets to the sweet farewell [Scattering flowers] I hop"d thou should"st have been my Hamlet"s wife I thought thy bride-bed to have deck"d, sweet maid, And not to have strew"d thy grave. "6 Shakespear was thoroughly a master of the mixed motives of human character, and he here shows us the Queen, who was so criminal in some respects, not without sensibility [80] and affection in other relations of life. - Ophelia is a character almost too exquisitely touching to be dwelt upon. Oh rose of May, oh flower too soon faded! Her love, her madness, her death, are described with the truest touches of tenderness and pathos. it is a character which nobody but Shakespear could have drawn in the way that he has done, and to the conception of which there is not even the smallest approach, except in some of the old romantic ballads. Her brother, Laertes, is a character we do not like so well: he is too hot and choleric, and somewhat rhodomontade. Polonius is a perfect character in its kind; nor is there any foundation for the objections which have been made to the consistency of this part. It is said that he acts very foolishly, and talks very sensibly. There is no inconsistency in that. Again, that he talks wisely at one time and foolishly at another; that his advice to Laertes is very excellent, and his advice to the King and Queen on the subject of Hamlet"s madness very ridiculous. But he gives the one as a father, and is sincere in it; he gives the other as mere courtier, a busy-body, and is accordingly officious, garrulous, and impertinent. In short, Shakespear has been accused of inconsistency in this and other characters, only because he has kept up the distinction which there is in nature, between the understandings and the moral habits of men, between the absurdity of their ideas and the absurdity of their motives. Polonius is not a fool, but he makes himself so. His folly, whether in his actions or speeches, comes under the head of impropriety of intention. We do not like to see our author"s plays acted, and least [81] of all "Hamlet". There is no play that suffers so much in being transferred to the stage. Hamlet himself seems hardly capable of being acted. Mr. Kemble unavoidably fails in this character from a want of ease and variety. The character of Hamlet is made up of undulating lines; it has the yielding flexibility of "a wave o" th" sea." Mr. Kemble plays it like a man in armour, with a determined inveteracy of purpose, in one undeviating straight line, which is as remote from the natural grace and refined susceptibility of t