/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 2 Define the key terms. a. Coeff... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 2

Define the key terms. a. Coefficient b. Constant term c. Like terms d. Term e. Variable term

Short Answer

Expert verified
Coefficient: Multiplier of variables. Constant term: Value without variables. Like terms: Terms with same variables and powers. Term: Single mathematical expression. Variable term: Term containing a variable.

Step by step solution

01

Define Coefficient

A coefficient is a numerical or constant multiplier of the variables in an algebraic expression. For example, in the term 7x, 7 is the coefficient.
02

Define Constant Term

A constant term is a value in an algebraic expression that does not change and has no variables attached to it. For example, in the expression 5x + 3, the number 3 is the constant term.
03

Define Like Terms

Like terms are terms in an algebraic expression that have the same variables raised to the same powers, but they can have different coefficients. For example, 3x and 5x are like terms because both include the variable x.
04

Define Term

A term is a single mathematical expression that can be a number, a variable, or the product of numbers and variables. For example, in the expression 4y + 7, both 4y and 7 are terms.
05

Define Variable Term

A variable term is a term that contains a variable. For example, in the term 6z, 6 is the coefficient, and z is the variable term.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

coefficient
In algebra, terms often include numbers and variables. The coefficient is the numerical part of a term. It multiplies the variable. For instance, in the expression 7x, the number 7 is the coefficient. It tells you how many times the variable x is being counted. Coefficients can be positive, negative, whole numbers, or fractions. They are essential for combining like terms in algebraic expressions.
constant term
A constant term is a term that does not have a variable. This means its value does not change. For example, in the algebraic expression 5x + 3, the number 3 is the constant term. Unlike terms with variables, constant terms stay the same no matter what values the variables might take. They are straightforward and help simplify algebraic operations.
like terms
Like terms are terms that have the same variable raised to the same power, although their coefficients can be different. For instance, in the expression 3x + 5x, both 3x and 5x are like terms because they both include the variable x. Identifying like terms helps in simplifying algebraic expressions, as they can be added or subtracted from one another.
term
A term in algebra is any single expression. It could be just a number, just a variable, or a combination of both. For example, in the expression 4y + 7, 4y and 7 are individual terms. Notice that terms are separated by the addition or subtraction operators in an expression. Recognizing individual terms is fundamental for solving and simplifying algebraic expressions.
variable term
A term that contains a variable is called a variable term. For example, in the term 6z, 6 is the coefficient, and z is the variable. Unlike constant terms, variable terms change their value depending on the value of the variable. Variable terms are crucial for creating and solving algebraic equations.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

a. write an equation that represents the given statement. b. solve the problem. Six less than a number is the same as 3 more than twice the number.

Apply the associative property of addition or multiplication to rewrite each expression. Then simplify the expression. $$9(5 k)$$

Solve the equation. $$11=-q$$

Combine the like terms. $$-5-11 p+23 p-p+4$$

Solve the equation using the multiplication or division properties of equality. $$-9=-n$$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.