如何求多项式的次数

下载PDF文件
下载PDF文件

多项式是指“含有很多项”，它可以是包含常数、变量和指数的不同形式的表达式。例如，x-2是一个多项式；25也是个多项式。要想求一个多项式的次数，只需找出多项式中最大的指数即可。 [1] 如果想找出不同多项式的次数，可按以下步骤进行。

部分 1
部分 1 的 3:

含一个变量或不含变量的多项式

下载PDF文件
  1. {"smallUrl":"https:\/\/www.wikihow.com\/images_en\/thumb\/1\/16\/Find-the-Degree-of-a-Polynomial-Step-1-Version-2.jpg\/v4-460px-Find-the-Degree-of-a-Polynomial-Step-1-Version-2.jpg","bigUrl":"https:\/\/www.wikihow.com\/images\/thumb\/1\/16\/Find-the-Degree-of-a-Polynomial-Step-1-Version-2.jpg\/v4-728px-Find-the-Degree-of-a-Polynomial-Step-1-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
    为了简化起见，请将表达式中所有的同类项进行合并。以 3x 2 - 3x 4 - 5 + 2x + 2x 2 - x为例，你只需把x 2 , x的所有同类项和常数项合并，就得到 2 - 3x 4 - 5 + x。
  2. {"smallUrl":"https:\/\/www.wikihow.com\/images_en\/thumb\/0\/06\/Find-the-Degree-of-a-Polynomial-Step-2-Version-2.jpg\/v4-460px-Find-the-Degree-of-a-Polynomial-Step-2-Version-2.jpg","bigUrl":"https:\/\/www.wikihow.com\/images\/thumb\/0\/06\/Find-the-Degree-of-a-Polynomial-Step-2-Version-2.jpg\/v4-728px-Find-the-Degree-of-a-Polynomial-Step-2-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
    常数项是指不含未知数的所有项，例如3或5。 系数是指未知数的数字因数。在求一个多项式的次数时，你可以主动忽略常数项和系数或把它们划掉。例如，5x 2 的系数是5，而它的次数与系数无关，所以不需要看系数。
  3. {"smallUrl":"https:\/\/www.wikihow.com\/images_en\/thumb\/f\/fc\/Find-the-Degree-of-a-Polynomial-Step-4-Version-2.jpg\/v4-460px-Find-the-Degree-of-a-Polynomial-Step-4-Version-2.jpg","bigUrl":"https:\/\/www.wikihow.com\/images\/thumb\/f\/fc\/Find-the-Degree-of-a-Polynomial-Step-4-Version-2.jpg\/v4-728px-Find-the-Degree-of-a-Polynomial-Step-4-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
    幂是指数的数值 [2] 。在例式
    -x 4 + x 2 + x中，第一项的幂值是4。因为你已将指数最大的项排在第一项，所以要找最大的幂值就在第一项里找。
  4. {"smallUrl":"https:\/\/www.wikihow.com\/images_en\/thumb\/e\/e8\/Find-the-Degree-of-a-Polynomial-Step-5-Version-2.jpg\/v4-460px-Find-the-Degree-of-a-Polynomial-Step-5-Version-2.jpg","bigUrl":"https:\/\/www.wikihow.com\/images\/thumb\/e\/e8\/Find-the-Degree-of-a-Polynomial-Step-5-Version-2.jpg\/v4-728px-Find-the-Degree-of-a-Polynomial-Step-5-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
    你可以写：该多项式的次数=4。或以更合适的形式写下： deg (3x 2 - 3x 4 - 5 + 2x + 2x 2 - x) = 3 ，这样就完成了。 [3]
  5. {"smallUrl":"https:\/\/www.wikihow.com\/images_en\/thumb\/7\/78\/Find-the-Degree-of-a-Polynomial-Step-6.jpg\/v4-460px-Find-the-Degree-of-a-Polynomial-Step-6.jpg","bigUrl":"https:\/\/www.wikihow.com\/images\/thumb\/7\/78\/Find-the-Degree-of-a-Polynomial-Step-6.jpg\/v4-728px-Find-the-Degree-of-a-Polynomial-Step-6.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
    如果一个多项式仅含常数，比如15或55，那么它的次数就是0。你可以想象该常数项含有一个变量，该变量的次数为0，而实际上是1。例如，你有一个常数是15，你可以把它想象成 15x 0 实际上就是15 x 1，或是15。这说明常数的次数为0。
    广告
部分 2
部分 2 的 3:

含多个变量的多项式

下载PDF文件
  1. {"smallUrl":"https:\/\/www.wikihow.com\/images_en\/thumb\/d\/de\/Find-the-Degree-of-a-Polynomial-Step-7.jpg\/v4-460px-Find-the-Degree-of-a-Polynomial-Step-7.jpg","bigUrl":"https:\/\/www.wikihow.com\/images\/thumb\/d\/de\/Find-the-Degree-of-a-Polynomial-Step-7.jpg\/v4-728px-Find-the-Degree-of-a-Polynomial-Step-7.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
    求含一个变量的多项式的次数相比求含多个变量的多项式的次数稍微复杂一点：
    • x 5 y 3 z + 2xy 3 + 4x 2 yz 2
  2. {"smallUrl":"https:\/\/www.wikihow.com\/images_en\/thumb\/b\/b2\/Find-the-Degree-of-a-Polynomial-Step-8.jpg\/v4-460px-Find-the-Degree-of-a-Polynomial-Step-8.jpg","bigUrl":"https:\/\/www.wikihow.com\/images\/thumb\/b\/b2\/Find-the-Degree-of-a-Polynomial-Step-8.jpg\/v4-728px-Find-the-Degree-of-a-Polynomial-Step-8.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
    仅将每一项中变量的次数相加，不用考虑不同的变量。需要记住未标记出来次数的变量，例如x或y的次数是1。按如下方法将三项中的变量次数逐一相加： [4]
    • x 5 y 3 z = 5 + 3 + 1 = 9
    • 2xy 3 = 1 + 3 = 4
    • 4x 2 yz 2 = 2 + 1 + 2 = 5
  3. {"smallUrl":"https:\/\/www.wikihow.com\/images_en\/thumb\/0\/09\/Find-the-Degree-of-a-Polynomial-Step-9.jpg\/v4-460px-Find-the-Degree-of-a-Polynomial-Step-9.jpg","bigUrl":"https:\/\/www.wikihow.com\/images\/thumb\/0\/09\/Find-the-Degree-of-a-Polynomial-Step-9.jpg\/v4-728px-Find-the-Degree-of-a-Polynomial-Step-9.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
    上面三项的最大次数值为9，是第一项的次数相加得到的数值。
  4. {"smallUrl":"https:\/\/www.wikihow.com\/images_en\/thumb\/1\/1f\/Find-the-Degree-of-a-Polynomial-Step-10.jpg\/v4-460px-Find-the-Degree-of-a-Polynomial-Step-10.jpg","bigUrl":"https:\/\/www.wikihow.com\/images\/thumb\/1\/1f\/Find-the-Degree-of-a-Polynomial-Step-10.jpg\/v4-728px-Find-the-Degree-of-a-Polynomial-Step-10.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
    9是整个多项式的次数。你可以写下最后答案： deg (x 5 y 3 z + 2xy 3 + 4x 2 yz 2 ) = 9
    广告
部分 3
部分 3 的 3:

有理式

下载PDF文件
  1. {"smallUrl":"https:\/\/www.wikihow.com\/images_en\/thumb\/9\/90\/Find-the-Degree-of-a-Polynomial-Step-11.jpg\/v4-460px-Find-the-Degree-of-a-Polynomial-Step-11.jpg","bigUrl":"https:\/\/www.wikihow.com\/images\/thumb\/9\/90\/Find-the-Degree-of-a-Polynomial-Step-11.jpg\/v4-728px-Find-the-Degree-of-a-Polynomial-Step-11.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
    以(x 2 + 1)/(6x -2)为例。 [5]
  2. {"smallUrl":"https:\/\/www.wikihow.com\/images_en\/thumb\/7\/7f\/Find-the-Degree-of-a-Polynomial-Step-12.jpg\/v4-460px-Find-the-Degree-of-a-Polynomial-Step-12.jpg","bigUrl":"https:\/\/www.wikihow.com\/images\/thumb\/7\/7f\/Find-the-Degree-of-a-Polynomial-Step-12.jpg\/v4-728px-Find-the-Degree-of-a-Polynomial-Step-12.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
    含分数的多项式求次数不需要系数或常数项。所以，要将分子里的1和分母里的6和-2去掉，得到x 2 /x。
  3. {"smallUrl":"https:\/\/www.wikihow.com\/images_en\/thumb\/b\/b1\/Find-the-Degree-of-a-Polynomial-Step-13.jpg\/v4-460px-Find-the-Degree-of-a-Polynomial-Step-13.jpg","bigUrl":"https:\/\/www.wikihow.com\/images\/thumb\/b\/b1\/Find-the-Degree-of-a-Polynomial-Step-13.jpg\/v4-728px-Find-the-Degree-of-a-Polynomial-Step-13.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
    分子的变量次数为2，分母的变量次数为1，所以用2减去1，即2-1=1。
  4. 你可以写：该有理式的次数是1，或者 deg [(x 2 + 1)/(6x -2)] = 1.
    {"smallUrl":"https:\/\/www.wikihow.com\/images_en\/thumb\/e\/ea\/Find-the-Degree-of-a-Polynomial-Step-14.jpg\/v4-460px-Find-the-Degree-of-a-Polynomial-Step-14.jpg","bigUrl":"https:\/\/www.wikihow.com\/images\/thumb\/e\/ea\/Find-the-Degree-of-a-Polynomial-Step-14.jpg\/v4-728px-Find-the-Degree-of-a-Polynomial-Step-14.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
    广告

小提示

  • 以上仅是你在大脑中想到的步骤，不需要在纸上写下来，当然如果是第一次做，写下来可能会有帮助，毕竟写下来不容易犯错。
  • 按照惯例，零多项式的次数被看作是负无穷大。
  • 在第三步中，例如x这样的线性项，可记为 x 1 ，而像7这样的非零常数项可记为7 x 。 0
广告

你可能还喜欢

如何
求直角三角形斜边的长度
如何
因式分解三次多项式
如何
使用算盘
如何
装病
如何
计算百分数
如何
计算功率
求三阶矩阵的逆矩阵
如何
计算三角形面积
如何
读尺子上的刻度
如何
计算三角形的周长
如何
计算角度
如何
解三次方程
如何
计算矩阵乘法
如何
按照APA格式引用英文网址
广告

参考

  1. ↑ http://www.mathwarehouse.com/algebra/polynomial/degree-of-polynomial.php
  2. ↑ http://www.mathsisfun.com/algebra/polynomials.html
  3. ↑ http://www.mathwarehouse.com/algebra/polynomial/degree-of-polynomial.php
  4. ↑ http://www.mathsisfun.com/algebra/degree-expression.html
  5. ↑ http://www.mathsisfun.com/algebra/degree-expression.html

关于本wikiHow

其他语言
本页面已经被访问过22,967次。

这篇文章对你有帮助吗？

广告