Consider The Following Expression:${ 5a + 4b + 3 }$Select All Of The True Statements Below.- { 5a $}$ Is A Factor.- 3 Is A Constant.- { 5a $}$ Is A Coefficient.- { 5a $}$ And 3 Are Like Terms.- [$ 5a +

Mar 10, 2025 by ADMIN 203 views

**Understanding Algebraic Expressions: A Closer Look at Factors, Constants, Coefficients, and Like Terms**

Introduction

Algebraic expressions are a fundamental concept in mathematics, and understanding their components is crucial for solving equations and manipulating variables. In this article, we will delve into the world of algebraic expressions, focusing on factors, constants, coefficients, and like terms. We will examine the given expression $5a + 4b + 3$ and determine which of the provided statements are true.

Factors

A factor is a number or variable that divides another number or expression without leaving a remainder. In the given expression $5a + 4b + 3$ , we can identify the factors as $5$ , $4$ , and $3$ . These numbers are factors because they can be multiplied together to obtain the original expression.

5 is a factor because it can be multiplied by a to obtain the term $5a$ .
4 is a factor because it can be multiplied by b to obtain the term $4b$ .
3 is a factor because it is a constant term in the expression.

Constants

A constant is a number that does not change value. In the given expression $5a + 4b + 3$ , the constant term is 3. This is because 3 is a fixed number that does not depend on any variable.

3 is a constant because it is a fixed number that does not change value.

Coefficients

A coefficient is a number that multiplies a variable. In the given expression $5a + 4b + 3$ , the coefficients are 5 and 4. These numbers multiply the variables a and b, respectively.

5 is a coefficient because it multiplies the variable a to obtain the term $5a$ .
4 is a coefficient because it multiplies the variable b to obtain the term $4b$ .

Like Terms

Like terms are terms that have the same variable(s) raised to the same power. In the given expression $5a + 4b + 3$ , the like terms are $5a$ and $4b$ . These terms have the same variable a and b, respectively.

5a and 4b are like terms because they have the same variable(s) raised to the same power.

Conclusion

In conclusion, we have examined the given expression $5a + 4b + 3$ and determined which of the provided statements are true. The true statements are:

5 is a factor.
3 is a constant.
5 is a coefficient.
4 is a coefficient.

The false statements are:

5a and 3 are like terms.
5a and 4b are like terms.

By understanding the components of algebraic expressions, we can better solve equations and manipulate variables. This knowledge is essential for success in mathematics and other fields that rely on algebraic expressions.

Final Thoughts

Algebraic expressions are a fundamental concept in mathematics, and understanding their components is crucial for solving equations and manipulating variables. By examining the given expression $5a + 4b + 3$ , we have identified the factors, constants, coefficients, and like terms. This knowledge will help you better understand algebraic expressions and improve your problem-solving skills.

References

Algebraic Expressions
Factors
Constants
Coefficients
Like Terms
Algebraic Expressions: A Q&A Guide =====================================

Introduction

Algebraic expressions are a fundamental concept in mathematics, and understanding their components is crucial for solving equations and manipulating variables. In this article, we will provide a Q&A guide to help you better understand algebraic expressions, factors, constants, coefficients, and like terms.

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. It is a way to represent a mathematical relationship between variables and constants.

Q: What are factors in an algebraic expression?

A: Factors in an algebraic expression are numbers or variables that divide another number or expression without leaving a remainder. In the expression $5a + 4b + 3$ , the factors are $5$ , $4$ , and $3$ .

Q: What is a constant in an algebraic expression?

A: A constant in an algebraic expression is a number that does not change value. In the expression $5a + 4b + 3$ , the constant is $3$ .

Q: What is a coefficient in an algebraic expression?

A: A coefficient in an algebraic expression is a number that multiplies a variable. In the expression $5a + 4b + 3$ , the coefficients are $5$ and $4$ .

Q: What are like terms in an algebraic expression?

A: Like terms in an algebraic expression are terms that have the same variable(s) raised to the same power. In the expression $5a + 4b + 3$ , the like terms are $5a$ and $4b$ .

Q: How do I identify like terms in an algebraic expression?

A: To identify like terms in an algebraic expression, look for terms that have the same variable(s) raised to the same power. For example, in the expression $5a + 4b + 3$ , the like terms are $5a$ and $4b$ because they both have the variable $a$ and $b$ raised to the power of 1.

Q: Can a constant be a factor?

A: Yes, a constant can be a factor. For example, in the expression $3a + 4b + 3$ , the constant $3$ is a factor because it can be multiplied by the variable $a$ to obtain the term $3a$ .

Q: Can a coefficient be a factor?

A: Yes, a coefficient can be a factor. For example, in the expression $5a + 4b + 3$ , the coefficient $5$ is a factor because it can be multiplied by the variable $a$ to obtain the term $5a$ .

Q: Can like terms be factors?

A: No, like terms cannot be factors. Like terms are terms that have the same variable(s) raised to the same power, while factors are numbers or variables that divide another number or expression without leaving a remainder.

Conclusion

In conclusion, we have provided a Q&A guide to help you better understand algebraic expressions, factors, constants, coefficients, and like terms. By understanding these concepts, you will be able to solve equations and manipulate variables with ease.

Final Thoughts

Algebraic expressions are a fundamental concept in mathematics, and understanding their components is crucial for solving equations and manipulating variables. By following this Q&A guide, you will be able to identify factors, constants, coefficients, and like terms in algebraic expressions and improve your problem-solving skills.