课程： 12.4 评价多元表达式

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选择节评价多元表达式

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评价多元表达式
Mr. Travis is taking his Social Studies class on a tour of downtown. He has created a scavenger hunt for the students as they travel around the city. The scavenger hunt is made up of all different types of architecture and landmarks as well as problems that will need to be solved. Mr. Travis asked the bus to drop the students off in front of the Town Hall. In the square across from the town hall is a plaza with three cubes in it.
::Travis先生正在市中心旅游,参加社会研究课程,他为学生们在城市周围旅行创建了寻宝游戏,寻宝游戏由各种建筑和地标以及需要解决的问题组成,Travis先生要求公共汽车将学生送到市政厅门前,在市政厅对面的广场上有三块立方块。

One of the problems on the sheet read “Before you is a cube. Use the formula $\begin{aligned} A = 6 s^{2} \end{aligned}$ to find the surface area of a cube whose side measures 8 feet.”
::工作表上的问题之一是“在您成为立方体之前。使用公式A=6s2来找到其侧边度为8英尺的立方体的表面面积。”

Can you solve this problem?
::你能解决这个问题吗?

In this concept, you will learn to evaluate polynomial expressions.
::在这个概念中,你将学会评价多元表达式。

Evaluating Polynomials
::评估多元性

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。

In order to solve algebraic expressions, you need to use the , commonly called PEMDAS . The diagram below shows the order of arithmetic operations performed using PEMDAS.
::为了解析代数表达式,您需要使用通常称为 PEMDAS 的代数表达式。下图显示了使用 PEMDAS 进行的算术操作的顺序。

When you consider expressions, you can evaluate an expression for a given value. In other words, you can find the total value if you know the value that corresponds to the variable . You can replace the variable(s) with the given value and then use the order of operations to calculate the total value.
::当您考虑表达式时,您可以对给定值的表达式进行评价。换句话说,如果您知道变量对应的值,您可以找到总值。您可以用给定值替换变量,然后使用操作顺序来计算总值。

Let’s look at an example.
::让我们举个例子。

Evaluate $\begin{aligned} x^{2} + 3 x - 10 \end{aligned}$ for $\begin{aligned} x = 5 \end{aligned}$
::x=5 评价 x2+3x- 10

First, replace the variables with the given value of $\begin{aligned} x \end{aligned}$ .
::首先,用 x 的给定值替换变量。

$\begin{aligned} (5)^{2} + 3 (5) - 10 \end{aligned}$

Next, find the total value using the order of operations.
::下一步,使用操作顺序查找总值。

$\begin{aligned} \begin{array}{rcl} (5)^{2} + 3 (5) - 10 \\ 25 + 3 (5) - 10 There is no group so start with the exponent . \\ 25 + 15 - 10 Complete the multiplication . \\ 40 - 10 Perform the addition and subtraction from left to right. \\ 30 \end{array} \end{aligned}$

:5)2+3(5)-1025+3(5)-10 没有组从前言25+15-10开始,完成乘数40-10完成从左到右的增减。

The answer is 30.
::答案是30岁

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about the cube. You have been asked to find the surface area of a cube that has a side length of 8 feet.
::早些时候,有人给了你一个有关立方体的问题。有人要求你找到一个立方体的表面区域,该立方体的侧长为8英尺。

First, substitute the side length into the formula for the surface area.
::首先,用公式的侧长代替表面积。

$\begin{aligned} \begin{array}{rcl} A & = & 6 s^{2} \\ A & = & 6 (8)^{2} \end{array} \end{aligned}$

::A=6s2A=6(8)2

Next, use PEMDAS to solve for the surface area.
::接下来,使用 PEMDAS 解析表层区域。

$\begin{aligned} \begin{array}{rcl} A & = & 6 (8)^{2} First evaluate the exponent 8^{2} = 8 \times 8 = 64. \\ A & = & 6 (64) Perform the multiplication. \\ A & = & 384 \end{array} \end{aligned}$

::A=6( 8) 2 第一次评价指数 82=8x8=64. A=6( 64) 应用乘法 A=384

The answer is 384.
::答案是384

The surface area of the cube is 384 ft ² .
::立方体的表面面积为384平方英尺。

Example 2
::例2

Evaluate $\begin{aligned} 4 x^{2} + 2 x + 15 \end{aligned}$ for $\begin{aligned} x = 3 \end{aligned}$
::x=3 的四x2+2x+15

First, replace the variables with the given value of $\begin{aligned} x \end{aligned}$ .
::首先,用 x 的给定值替换变量。

$\begin{aligned} 4 (3)^{2} + 2 (3) + 15 \end{aligned}$

Next, find the total value using the order of operations.
::下一步,使用操作顺序查找总值。

$\begin{aligned} \begin{array}{rcl} 4 (3)^{2} + 2 (3) + 15 \\ 4 (9) + 2 (3) + 15 There is no group so start with the exponent . \\ 36 + 6 + 15 Complete the multiplication . \\ 42 + 15 Perform the addition from left to right. \\ 57 \end{array} \end{aligned}$

::4(3)2+2(3)+154(9)+2(3)+15 没有组别, 因此从前言者开始36+6+15 完成乘数 42+15 执行从左到右的添加。

The answer is 57.
::答案是57。

Example 3
::例3

Evaluate $\begin{aligned} x^{2} + 5 x - 1 \end{aligned}$ for $\begin{aligned} x = 3 \end{aligned}$
::x=3 评价 x2+5x-1

First, replace the variables with the given value of $\begin{aligned} x \end{aligned}$ .
::首先,用 x 的给定值替换变量。

$\begin{aligned} (3)^{2} + 5 (3) - 1 \end{aligned}$

Next, find the total value using the order of operations.
::下一步,使用操作顺序查找总值。

$\begin{aligned} \begin{array}{rcl} (3)^{2} + 5 (3) - 1 \\ (9) + 5 (3) - 1 There is no group so start with the exponent . \\ 9 + 15 - 1 Complete the multiplication. \\ 24 - 1 Perform the addition and subtraction from left to right. \\ 23 \end{array} \end{aligned}$

:3)2+5(3)-1(9)+5(3)-1没有组别,因此从引号9+15-1开始,完成乘数24-1完成从左到右的增减。

The answer is 23.
::答案是23岁

Example 4
::例4

Evaluate $\begin{aligned} x^{2} + 4 x - 9 \end{aligned}$ for $\begin{aligned} x = 2 \end{aligned}$
::x=2 评价 x2+4x-9

First, replace the variables with the given value of $\begin{aligned} x \end{aligned}$ .
::首先,用 x 的给定值替换变量。

$\begin{aligned} (2)^{2} + 4 (2) - 9 \end{aligned}$

Next, find the total value using the order of operations.
::下一步,使用操作顺序查找总值。

$\begin{aligned} \begin{array}{rcl} (2)^{2} + 4 (2) - 9 \\ (4) + 4 (2) - 9 There is no group so start with the exponent . \\ 4 + 8 - 9 Complete the multiplication. \\ 12 - 9 Perform the addition and subtraction from left to right. \\ 3 \end{array} \end{aligned}$

:2)2+4(2)-9(4)+4(2)-9没有组别,因此从引号4+8-9开始,完成乘数。 12-9 执行从左到右的增减。

The answer is 3.
::答案是3

Example 5
::例5

Evaluate $\begin{aligned} 2 x^{2} + 2 x + 5 \end{aligned}$ for $\begin{aligned} x = 3 \end{aligned}$
::x=3 的 2x2+2x+5

First, replace the variables with the given value of $\begin{aligned} x \end{aligned}$ .
::首先,用 x 的给定值替换变量。

$\begin{aligned} 2 (3)^{2} + 2 (3) + 5 \end{aligned}$

Next, find the total value using the order of operations.
::下一步,使用操作顺序查找总值。

$\begin{aligned} \begin{array}{rcl} (3)^{2} + 2 (3) + 5 \\ 2 (9) + 2 (3) + 5 There is no group so start with the exponent . \\ 18 + 6 + 5 Complete the multiplication . \\ 24 + 5 Addition from left to right. \\ 29 \end{array} \end{aligned}$

:3)2+2(3)+52(9)+2(3)+5没有组别,因此没有组别从前言方开始。 18+6+5完成乘数24+5从左到右。

The answer is 29.
::答案是29。

Review
::回顾

Evaluate the following expressions for the given value.
::评估给定值的下列表达式。

$\begin{aligned} 7 x^{3} \end{aligned}$ for $\begin{aligned} x = 2 \end{aligned}$
::x=2 的 7x3

$\begin{aligned} 6 x^{2} \end{aligned}$ for $\begin{aligned} x = 3 \end{aligned}$
::x=3 的 6x2

$\begin{aligned} 4 x^{3} \end{aligned}$ for $\begin{aligned} x = 2 \end{aligned}$
::x=2 的 4x3

$\begin{aligned} 8 x^{2} \end{aligned}$ for $\begin{aligned} x = 2 \end{aligned}$
::x=2 的 8x2

$\begin{aligned} 10 x y \end{aligned}$ for $\begin{aligned} x = 2, y = 3 \end{aligned}$
::x=2, y=3 10xy

$\begin{aligned} 7 x^{2} + 4 x \end{aligned}$ for $\begin{aligned} x = 2 \end{aligned}$
::x=2 的 7x2+4x

$\begin{aligned} 6 x^{2} + 5 x \end{aligned}$ for $\begin{aligned} x = 2 \end{aligned}$
::x=2 的 6x2+5x

$\begin{aligned} 3 x^{2} + 8 x \end{aligned}$ for $\begin{aligned} x = 3 \end{aligned}$
::x=3 的 3x2+8x

$\begin{aligned} 7 x^{2} + 4 x - 2 \end{aligned}$ for $\begin{aligned} x = 2 \end{aligned}$
::x=2 的 7x2+4x-2

$\begin{aligned} 9 x^{2} + 5 x - 3 \end{aligned}$ for $\begin{aligned} x = 3 \end{aligned}$
::x=3 的 9x2+5x-3

$\begin{aligned} 5 x^{2} + 5 x - 2 \end{aligned}$ for $\begin{aligned} x = 2 \end{aligned}$
::x=2 5x2+5x-2

$\begin{aligned} 12 x^{2} + 8 x + 11 \end{aligned}$ for $\begin{aligned} x = 2 \end{aligned}$
::x=2 的 12x2+8x+11

$\begin{aligned} 6 y^{2} - 2 y - 8 \end{aligned}$ for $\begin{aligned} y - 6 \end{aligned}$
::y-6 6y2-2y-8 y-6

$\begin{aligned} 3 (x - 7) + 5 (x + 1) \end{aligned}$ for $\begin{aligned} x = 10 \end{aligned}$
::x=10的3(x-7)+5(x+1)

$\begin{aligned} - 2 y^{3} + 6 (y - 4) + y \end{aligned}$ for $\begin{aligned} y = - 3 \end{aligned}$
::-2y3+6(y-4)+yyyyy=3 y=3 y=2y3+6(y-4)+y=3

Review (Answers)
::回顾(答复)

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。

Resources
::资源

章节大纲

常规

评价多元表达式

Evaluating Polynomials ::评估多元性

Examples ::实例

Example 1 ::例1

Example 2 ::例2

Example 3 ::例3

Example 4 ::例4

Example 5 ::例5

Review ::回顾

Review (Answers) ::回顾(答复)

Resources ::资源

Evaluating Polynomials
::评估多元性

Examples
::实例

Example 1
::例1

Example 2
::例2

Example 3
::例3

Example 4
::例4

Example 5
::例5

Review
::回顾

Review (Answers)
::回顾(答复)

Resources
::资源