What are terms, factors, and coefficients in algebraic expressions? | 6th grade | Khan Academy

TL;DR

Learn the key terms used to describe expressions, including terms, factors, and coefficients.

Transcript

What I want to do in this video is think about how expressions are formed and the words we use to describe the different parts of an expression. And the reason why this is useful is when you hear other people refer to some expression and say, oh, I don't agree with the second term, or the third term has four factors, or why is the coefficient on th... Read More

Key Insights

• 😑 Terms are the parts of an expression that are being added or subtracted.
• 🧑‍🏭 Factors are the things being multiplied in each term.
• 😣 Coefficients are the constants that multiply the rest of the term.
• 😑 Expressions can have multiple levels of terms and factors, depending on the nesting of the expression.
• 😑 Variables and constants can be considered factors in an expression.
• 🗂️ Dividing by a variable is the same as multiplying by its reciprocal.
• 🧑‍🏭 Exponents in variables are traditionally considered as one factor.

Questions & Answers

Q: What are terms in an expression?

Terms are the parts of an expression that are being added or subtracted. They can include constants, variables, and their products.

Q: How do you determine the factors of a term?

Factors are the things being multiplied in each term. To find the factors, you can look at the variables and constants that are being multiplied together.

Q: What is a coefficient in an expression?

The coefficient is the nonvariable that multiplies the rest of the term. It is a constant value that appears in front of the variables.

Q: Can expressions have multiple levels of terms and factors?

Yes, expressions can have nested terms and factors. A smaller expression can act as a factor within a larger expression, and each level can have its own set of terms and factors.

Summary & Key Takeaways

• An expression is made up of terms, which are the parts that are being added or subtracted.

• Factors are the things being multiplied in each term, and coefficients are the constants that multiply the rest of the term.

• Expressions can have multiple levels of terms and factors, depending on the nesting of the expression.