Section outline

  • In this chapter, we learned about:
    ::在本章中,我们了解到:

    What Is a Polynomial Function?
    ::什么是多面函数?

    • A function is a polynomial function if it is the sum or difference of terms with real coefficients and non-negative integer powers. Important parts of a polynomial function include the degree, the lead term, the lead coefficient, and the constant term.
      ::如果函数是实际系数和非负整数功率的总和或条件差异,则函数是一种多数值函数。多数值函数的重要部分包括程度、牵头条件、牵头系数和常数。

    Adding or Subtracting Polynomials
    ::添加或减减多元数

    • To add polynomials, identify the like terms and add their coefficients.
      ::添加多语种, 标明类似术语, 并添加系数 。
    • To subtract polynomials, distribute -1 to each term in the second polynomial, then follow the steps for addition.
      ::要减去多面体,则在第二个多面体中将 - 1 分配到每个术语,然后遵循添加步骤。

    Multiplying Polynomials
    ::乘以多边多边形

    • To multiply a monomial by a polynomial, distribute the monomial to each one of the terms in the polynomial and use the product rule of exponents.
      ::将单体乘以多面体,将单体体分解为多面体中的每个术语,并使用推手的产品规则。
    • To multiply a binomial by a binomial, use the FOIL method to organize distributing the terms in the first binomial to the second binomial.
      ::将二进制乘以二进制, 使用FOIL方法来组织将第一个二进制的术语 分配给第二个二进制的术语。
    • There are three ways to organize multiplying polynomials by polynomials: horizontally, vertically, or the chart method.
      ::有三种方法通过多面体组织乘数多面体:水平、垂直或图表方法。
    • To multiply polynomials, distribute each term in the first polynomial to the second polynomial, then combine like terms.
      ::乘以多义, 在第一个多义中将每个词分布到第二个多义中, 然后将类似术语合并起来 。

    Dividing Polynomials
    ::分裂的多面体

    • To divide polynomials, approach it similar to dividing numbers. However, instead of using the highest place value, we use the highest degree term.
      ::要分割多种族, 请使用和分隔数字相似的方法。 但是, 我们不是使用最高位值, 而是使用最高位值 。
    • To divide polynomials when the divisor is of the form lx−k, determine the number to put in the box, list the coefficients of the dividend, pull down the first coefficient, multiply that number with the number in the box, put the result in the next column and add the numbers in the column. Repeat this process until there are no columns remaining.
      ::要在以 lx- k 格式的边框中分隔多数值, 确定要放入框中的数字, 列出红利的系数, 拉下第一个系数, 将该数值乘以框中的数字, 将结果放入下一列, 并在列中添加数字。 重复此进程, 直到没有剩余列 。

    Performing Operations on Functions
    ::在函数上执行操作

    • To add, subtract, multiply or divide functions, replace the functions with their rules and perform the operations.
      ::添加、减、乘或分割功能,用其规则替换功能,并进行操作。
    • To compose two functions, input one function into the other function.
      ::要组成两个函数,则将一个函数输入到另一个函数中。
    • The domain of compositions is the intersection of the domain of the input function and the domain of the result of the composition.
      ::构成域是输入函数域与构成结果域的交叉点。

    Looking Back, Looking Forward
    ::回顾,展望未来

    In this chapter, we covered an important class of functions called polynomial functions. We added, subtracted, multiplied, and divided them and then generalized those ideas to doing those operations with other functions. We also lear ned a new operation called composition. We will see composition again when we discuss inverse functions.
    ::在本章中,我们覆盖了一种重要功能类别,称为多重函数。我们添加、减减、乘、分,然后将这些想法推广到以其他功能进行这些操作。我们还学会了一个新的行动,称为构成。当我们讨论反函数时,我们将再次看到组成。

    In the next chapter, we will cover factoring polynomials. Factoring polynomials is similar to factoring a number into its prime factors. We will see how this allows us to recognize an important part of the polynomial graph, the x- intercepts. 
    ::在下一章中,我们将涵盖多数值因素。多数值因素因素与将数因素因素纳入主要因素类似。我们将会看到这如何使我们能够识别多数值图的一个重要部分,即 X 界面。

    Chapter  Review
    ::回顾章次审查