Degree Of A Monomial - Varsity Tutors

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Degree of a Monomial

Study Guide

Key Definition

The degree of a monomial is the sum of the exponents of all its variables. For example, the degree of the monomial $7y^3z^2$ is $5$ because $3 + 2 = 5$.

Important Notes

  • The degree of a constant is always $0$.
  • For a monomial like $7x$, the degree is $1$.
  • The degree of $66$ is $0$.
  • In the expression $7y^3z^2$, add the exponents of $y$ and $z$.
  • Remember, no variable means the degree is $0$.
  • The degree of a nonzero constant is $0$; the zero monomial's degree is undefined.

Mathematical Notation

$+$ represents addition$-$ represents subtraction$\times$ or $*$ represents multiplication$\div$ or $/$ represents division$y^n$ indicates y raised to the power nRemember to use proper notation when solving problems

Why It Works

The degree of a monomial provides a quick way to understand the highest power of the variable terms, which is crucial for understanding polynomial behavior and solving equations involving monomials.

Remember

The degree of a monomial is the sum of its variable exponents.

Quick Reference

Degree of a nonzero constant:$0$Degree of a single-variable monomial:$n$ where n is the exponentDegree of $7y^3z^2$:$5$

Understanding Degree of a Monomial

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concept. Use space or enter to play video.concept thumbnailBeginner

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Beginner Explanation

The degree of a monomial is simply the sum of the exponents of all its variables. For example, in $7x^2$, the degree is $2$.Now showing Beginner level explanation.

Practice Problems

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1

Quick Quiz

Single Choice QuizBeginner

What is the degree of the monomial $6x^3y^2$?

A$5$B$6$C$3$D$0$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Degree Calculation

Compute the degree of the monomial $x^2y^3$.Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

Consider the monomial $5x^4y$. How would the degree change if the exponent of $y$ was increased by $2$?

Show AnswerClick to reveal the detailed explanation for this thinking exercise.4

Challenge Quiz

Single Choice QuizAdvanced

Determine the degree of the monomial $3x^2y^4z^5$.

A$11$B$10$C$9$D$12$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.

Recap

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