Problem 8 Determine whether each is a mono... [FREE SOLUTION]

91影视

Chapter 6: Problem 8

Determine whether each is a monomial, a binomial, or a trinomial. $$-w^{3}$$

Short Answer

Expert verified

The given expression $-w^3$ has only one term, and therefore, it is a monomial.

Step by step solution

Write down the given expression

The given expression is $-w^3$.

Identify the number of terms

$-w^3$ has only one term.

Determine the type of expression

Since $-w^3$ has one term, it is a monomial.

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.

Algebraic Expressions

Algebraic expressions are a way to express numbers and operations using symbols, typically involving variables, constants, and arithmetic operations. They play a crucial role in mathematics by allowing us to represent complex relationships in a simplified form.
An algebraic expression can consist of:

Variables: Letters that represent unknown values (e.g., $x$, $y$, $z$).
Constants: Numbers with a fixed value (e.g., 2, -7, 123).
Arithmetic Operations: Operations such as addition, subtraction, multiplication, and division.

These elements combine to form expressions like $3x + 5$, $2y - 4z + 7$, or in our exercise, $-w^3$.
Algebraic expressions are used in equations and inequalities that model real-world scenarios, allowing us to solve for unknowns.

Polynomials

A polynomial is a specific type of algebraic expression composed of terms that can include variables of different powers and coefficients. Each term in a polynomial should involve the variable raised to a whole number power.
Key points about polynomials include:

Terms: Polynomials consist of terms that are added or subtracted (e.g., $3x^2 + 2x - 5$).
Degree: The degree of a polynomial is the highest power of the variable in the expression. For example, $3x^2 + 2x - 5$ is a quadratic polynomial (degree 2).
Types: Polynomials are categorized based on the number of terms:
- Monomial: A single term, such as $-w^3$.
- Binomial: Two terms, such as $x + 1$.
- Trinomial: Three terms, such as $x^2 - 4x + 4$.

The expression $-w^3$ is a monomial (having one term) as it consists of a single variable term with a negative sign.

Mathematical Terms

Understanding mathematical terms is essential for grasping algebraic concepts. Here, we break down some key terms involved in algebraic expressions:

Coefficient: A number that multiplies a variable. For example, in $-w^3$, the coefficient is -1.
Term: A part of an expression separated by addition or subtraction. In our case, $-w^3$ is a single term.
Exponent: The power to which a variable is raised. The term $-w^3$ has an exponent of 3.
Variable: A symbol representing an unknown value, such as $w$ in $-w^3$.

Each of these components plays a vital role in shaping how we interpret and solve algebraic expressions. Understanding these basic terms allows us to categorize and solve expressions more effectively.

One App. One Place for Learning.

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

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Determine whether each is a monomial, a binomial, or a trinomial. $$-w^{3}$$

Short Answer

Step by step solution

Write down the given expression

Identify the number of terms

Determine the type of expression

Key Concepts

Algebraic Expressions

Polynomials

Mathematical Terms

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Discrete Mathematics

Probability and Statistics

Logic and Functions

Calculus

Decision Maths

Study anywhere. Anytime. Across all devices.