12.2 在标准表格中写入并分类多面体

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  在标准表格中写入并分类聚合

  

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  In this concept, you will learn to write and classify polynomials in standard form .
  ::在此概念中,您将学习以标准格式编写和分类多元动物。

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  Polynomials
  ::多元数

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  A polynomial is an algebraic expression that shows the sum of monomials.
  ::多面体是一种代数表达式,表示单面体的总和。

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  Here are some .
  ::这里有一些。

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  $\begin{align*}x^2+5 \quad \quad 3x-8+4x^5 \quad \quad -7a^2+9b-4b^3+6\end{align*}$
  ::x2+53x-8+4x5-7a2+9b-4b3+6

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  An expression with a single term is a monomial , an expression with two terms is a binomial , and an expression with three terms is a trinomial . An expression with more than three terms is named simply by its number of terms.
  ::单用一个术语的表达方式是一个单一术语,两个术语的表达方式是一个二进制术语,三个术语的表达方式是一个三进制术语。三个以上术语的表达方式仅按其术语编号命名。

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  First, let’s think about how you can classify each polynomial. You classify them according to terms. Each term can be classified by its degree .
  ::首先,让我们想想你如何对每个多元性进行分类。你按术语进行分类。每个术语都可以按其等级进行分类。

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  The degree of a term is determined by the exponent of the variable or the sum of the exponents of the variables in that term.
  ::术语的程度由变量的指数或该术语中变量的指数总和决定。

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  The expression $\begin{align*}x^2\end{align*}$  has an exponent of 2, so it is a term to the second degree.
  ::表达式 x2 的缩略语为 2 , 所以是二度的术语 。

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  The expression $\begin{align*}-2x^5\end{align*}$  has an exponent of 5, so it is a term to the fifth degree.
  ::- 2x5 表达式的出处为 5 , 所以是 5 级的术语 。

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  The expression $\begin{align*}x^2y\end{align*}$  has an exponent of 2 on the $\begin{align*}x\end{align*}$  and an unwritten exponent of 1 on the $\begin{align*}y\end{align*}$ , so this term is to the third degree $\begin{align*}(2 + 1)\end{align*}$ . Notice that you add the two degrees together because it has two variables.
  ::表达式 x2y 在 x 上有2 的引号, 在 y 上则有 1 的未写出引号, 所以这个词是 3 度 (2+1) 。 请注意, 您将两个度加在一起, 因为它有两个变量 。

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  The expression 8 is a monomial that is a constant with no variable, its degree is zero.
  ::表达式 8 是一个单数, 是一个不变, 没有变量, 其度为零 。

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  You can also work on the ways that you write polynomials. One way to write a polynomial is in standard form . In order to write any polynomial in standard form, you look at the degree of each term. You then write each term in order of degree, from highest to lowest, left to right .
  ::您也可以研究您写多边名词的方式。 一种写多边名词的方式是标准格式。 为了以标准格式写任何多边名词, 您可以查看每个术语的等级。 然后您将每个术语的等级依次写入, 从最高到最低, 从左到右。

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  Let’s look at an example.
  ::让我们举个例子。

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  Write the expression $\begin{align*}3x-8+4x^5\end{align*}$  in standard form.
  ::将表达式 3x-8+4x5 写入标准格式。

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  First, look at the degrees for each term in the expression.
  ::首先,看看表达式中每个词的度。

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  $\begin{align*}3x\end{align*}$  has a degree of 1
  ::3x 3x 有 1 度

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  8 has a degree of 0
  ::8 8 的度为 0

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  $\begin{align*}4x^5\end{align*}$  has a degree of 5
  ::4x5 级为 5

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  Next, write this trinomial in order by degree, highest to lowest
  ::接下来,写下这三部曲, 按程度排列, 最高到最低

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  $\begin{align*}4x^5+3x-8\end{align*}$
  ::4x5+3x-8

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  The answer is $\begin{align*}4x^5+3x-8\end{align*}$ .
  ::答案是4x5+3x-8。

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  The degree of a polynomial is the same as the degree of the highest term, so this expression is called a fifth degree trinomial.
  ::多元度与最高值相同,所以这个表达方式称为五度三角。

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  Examples
  ::实例

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  Example 1
  ::例1

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  Earlier, you were given a problem about  Erin and the polynomial.
  ::早些时候,你被问及艾琳和多民族主义的问题。

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  Erin has to identify the degree of the polynomial $\begin{align*}4x^3+3x+9\end{align*}$ .
  ::Erin必须确定4x3+3x+9的多边4x3+9的水平。

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  First, look at the degrees for each term in the expression.
  ::首先,看看表达式中每个词的度。

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  $\begin{align*}4x^3\end{align*}$  has a degree of 3
  ::4x3 度为 3

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  $\begin{align*}3x\end{align*}$  has a degree of 1
  ::3x 3x 有 1 度

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  $\begin{align*}9\end{align*}$  has a degree of 0
  ::9 度为0

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  Next, the highest degree identifies the degree of the polynomial.
  ::其次,最高学位确定多面性的程度。

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  The term $\begin{align*}4x^3\end{align*}$  is the highest degree so the degree of the polynomial is 3.
  ::4x3是最高等级,因此多元等级为3。

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  The answer is that the polynomial is of the third degree.
  ::答案是,多元体是三级。

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  Example 2
  ::例2

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  Write the following polynomial in standard form.
  ::以标准格式写下以下多边协议。

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  $\begin{align*}4x^3+3x^5+9x^4-2xy+11\end{align*}$
  ::4x3+3x5+9x4-2xy+11

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  First, look at the degrees for each term in the expression.
  ::首先,看看表达式中每个词的度。

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  $\begin{align*}4x^3\end{align*}$  has a degree of 3
  ::4x3 度为 3

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  $\begin{align*}3x^5\end{align*}$  has a degree of 5
  ::3x5 具有5度

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  $\begin{align*}9x^4\end{align*}$  has a degree of 4
  ::9x4 度为 4

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  $\begin{align*}-2xy\end{align*}$  has a degree of 2
  ::-2xy 具有2度

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  11 has a degree of 0
  ::11 的度为 0

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  Next, write this polynomial in order by degree, highest to lowest
  ::下一步, 写入此多面性, 按程度顺序排列, 最高到最低

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  $\begin{align*}3x^5+9x^4+4x^3-2xy+11\end{align*}$
  ::3x5+9x4+4x3-2xy+11

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  The answer is $\begin{align*}3x^5+9x^4+4x^3-2xy+11\end{align*}$ .
  ::答案是 3x5+9x4+4x3-2xy+11。

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  Example 3
  ::例3

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  Name the degree of the expression $\begin{align*}5x^4+3x^3+9x^2\end{align*}$ .
  ::命名表达式 5x4+3x3+9x2 的度。

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  First, look at the degrees for each term in the expression.
  ::首先,看看表达式中每个词的度。

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  $\begin{align*}5x^4\end{align*}$  has a degree of 4
  ::5x4 4 度为 4

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  $\begin{align*}3x^3\end{align*}$  has a degree of 3
  ::3x3 度为 3

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  $\begin{align*}9x^2\end{align*}$  has a degree of 2
  ::9x2 度为 2

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  Next, the highest degree identifies the degree of the polynomial.
  ::其次,最高学位确定多面性的程度。

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  The term $\begin{align*}5x^4\end{align*}$  is the highest degree so the degree of the polynomial is 4.
  ::5x4是最高等级,因此,多元等级为4。

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  The answer is that the polynomial is of the fourth degree.
  ::答案是,多元体是四度。

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  Example 4
  ::例4

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  Name the degree of the expression $\begin{align*}6y^3+3xy+9\end{align*}$ .
  ::命名表达式 6y3+3xy+9 的度。

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  First, look at the degrees for each term in the expression.
  ::首先,看看表达式中每个词的度。

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  $\begin{align*}6y^3\end{align*}$  has a degree of 3
  ::6y3 级为 3

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  $\begin{align*}3xy\end{align*}$  has a degree of 2
  ::3xy 3xy 有2度

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  $\begin{align*}9\end{align*}$  has a degree of 0
  ::9 度为0

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  Next, the highest degree identifies the degree of the polynomial.
  ::其次,最高学位确定多面性的程度。

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  The term $\begin{align*}6y^3\end{align*}$  is the highest degree so the degree of the polynomial is 3.
  ::6y3是最高学位,因此,多种族的等级是3。

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  The answer is that the polynomial is of the third degree.
  ::答案是,多元体是三级。

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  Example 5
  ::例5

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  Write the following polynomial in standard form and identify the degree of the polynomial.
  ::以标准形式写下以下多义,并确定多义的程度。

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  $\begin{align*}7x^2+3x-2x^4+8x^6-7\end{align*}$
  ::7x2+3x-2x4+8x6-7

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  First, look at the degrees for each term in the expression.
  ::首先,看看表达式中每个词的度。

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  $\begin{align*}7x^2\end{align*}$  has a degree of 2
  ::7x2 度为 2

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  $\begin{align*}3x\end{align*}$  has a degree of 1
  ::3x 3x 有 1 度

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  $\begin{align*}-2x^4\end{align*}$  has a degree of 4
  ::− 2x4 的度为 4

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  $\begin{align*}8x^6\end{align*}$  has a degree of 6
  ::8x6 具有6度6

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  $\begin{align*}-7\end{align*}$  has a degree of 0
  ::-7 度为0

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  Next, write this polynomial in order by degree, highest to lowest
  ::下一步, 写入此多面性, 按程度顺序排列, 最高到最低

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  $\begin{align*}8x^6-2x^4+7x^2+3x-7\end{align*}$
  ::8x6-2x4+7x2+3x-7

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  Then, the highest degree identifies the degree of the polynomial.
  ::然后,最高学位确定多民族的等级。

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  The term $\begin{align*}8x^6\end{align*}$  is the highest degree so the degree of the polynomial is 6.
  ::8x6 是最高等级, 多元等级为 6 。

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  The answer is $\begin{align*}8x^6-2x^4+7x^2+3x-7\end{align*}$  and the polynomial is of the sixth degree.
  ::答案是 8x6-2x4+7x2+3x-7,多元度为六度。

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  Review
  ::回顾

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  Write the following polynomials in standard form and then identify its degree:
  ::以标准格式写下以下多义,然后确定其程度:

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  1.  $\begin{align*}4x^2+5x^3+x-1\end{align*}$
  ::1. 4x2+5x3+x-1

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  2.  $\begin{align*}9+3y^2-2y\end{align*}$
  ::2. 9+3y2-2yy

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  3.  $\begin{align*}8+3y^3+8y+9y^2\end{align*}$
  ::3. 8+3y3+8y+9y2

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  4.  $\begin{align*} y+6y^4-2y^3+y^2\end{align*}$
  ::4. y+6y4 - 2y3+y2

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  5.  $\begin{align*}-16y^6-18\end{align*}$
  ::5.-16y6-18

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  6.  $\begin{align*}3x+2x^2+9y+8\end{align*}$
  ::6. 3x+2x2+9y+8

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  7.  $\begin{align*}8y^4+y-7y^3-3y^2\end{align*}$
  ::7. 8y4+y-7y3-3-3y2

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  8.  $\begin{align*}-3+8x^2-2x^3-x\end{align*}$
  ::8.-3+8x2-2x3-x

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  9.  $\begin{align*}9-3y^2-2y^3+2y\end{align*}$
  ::9-3y2-2-2y3+2yy

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  10.  $\begin{align*}14+6x^2-2x-8y\end{align*}$
  ::10. 14+6x2-2-2x-8y

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  11.  $\begin{align*}4x+3x^2-5x^3+8x^4\end{align*}$
  ::11. 4x+3x2-5x3+8x4

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  12.  $\begin{align*}-8+3y^2-2y^3+y\end{align*}$
  ::12.-8+3y2-2y3+y

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  13.  $\begin{align*}9+8y^2+2y^3-8y\end{align*}$
  ::13. 9+8y2+2y3-8y

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  14.  $\begin{align*}m^4-12m^7+6m^5-6m-8\end{align*}$
  ::14.4-12m7+6m5-6m-8

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  15.  $\begin{align*}-x^3y^2+5x^3y+8xy\end{align*}$
  ::15.-x3y2+5x3y+8xy

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  Review (Answers)
  ::回顾(答复)

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  Click to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
  ::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。

   

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  Resources
  ::资源