Problem 150 In the following exercises, iden... [FREE SOLUTION]

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Chapter 1: Problem 150

In the following exercises, identify the terms in each expression. $$ 11 x^{2}+8 x+5 $$

Short Answer

Expert verified

11x虏, 8x, 5

Step by step solution

Understand the Problem

Identify the terms in the polynomial expression given, which is: \[ 11x^{2} + 8x + 5 \]

Identify Terms in Polynomial

A term in a polynomial is a product of a constant and variable(s). For the expression $ 11x^{2} + 8x + 5 $, each part separated by the plus sign is a term.

List Each Term

The expression $ 11x^{2} + 8x + 5 $ has three terms: 1. $ 11x^{2} $ 2. $ 8x $ 3. $ 5 $

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

polynomial expression

A polynomial expression is a type of algebraic expression consisting of variables, coefficients, and non-negative integer exponents. Each component within the expression plays a specific role. For instance, in the polynomial expression \[ 11x^{2} + 8x + 5 \], we have:

Variables, represented by $ x $
Coefficients, which are the numbers in front of the variables, like 11 and 8
Constants, which are numbers without variables; in this case, 5

The polynomial expression's overall structure is essential for identifying and working with different terms in algebra.

terms identification

Identifying terms in a polynomial expression involves recognizing distinct parts separated by addition or subtraction signs. Each part, or term, in a polynomial can include:

Constants: Standalone numbers, like 5
Variables: Letters that represent numbers, like $ x $
Coefficients: Numbers multiplied by the variables, like 11 in $ 11x^{2} $

In the polynomial \[ 11x^{2} + 8x + 5 \], we can see three terms:

$ 11x^{2} $: A coefficient (11), and a variable $ x $ squared
$ 8x $: A coefficient (8), and a variable $ x $
5: A standalone constant term

Recognizing these terms is crucial for further algebraic operations.

algebra basics

Understanding basic algebra concepts helps in solving polynomial expressions. Here are a few key elements:

Variables: Symbols like $ x $ that represent numbers and can change value
Constants: Fixed values like 5 that do not change
Coefficients: Numbers that multiply the variables, such as 11 and 8 in our example
Exponents: Numbers that show how many times to multiply the variable by itself, seen in $ 11x^{2} $

By mastering these basics, one can efficiently break down and analyze any polynomial expression. Identifying and understanding different algebraic terms and their roles will help in simplifying, solving, and manipulating expressions effectively.

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91影视

In the following exercises, identify the terms in each expression. $$ 11 x^{2}+8 x+5 $$

Short Answer

Step by step solution

Understand the Problem

Identify Terms in Polynomial

List Each Term

Key Concepts

polynomial expression

terms identification

algebra basics

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