/*! 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 74 Classify each polynomial as a mo... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 74

Classify each polynomial as a monomial, a binomial, a trinomial, or none of these. $$x^{3}$$

Short Answer

Expert verified
The polynomial \(x^{3}\) is a monomial.

Step by step solution

01

Identify the number of terms

First, count the number of distinct terms in the polynomial. In \(x^{3}\), there is only one term.
02

Classify the polynomial

Next, classify the polynomial based on the number of terms identified in Step 1. A polynomial with one term is classified as 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.

Monomial
A monomial is the simplest form of a polynomial, consisting of a single term. It typically involves variables and coefficients, but always without addition or subtraction separating different terms within the polynomial. For example, in \(\(x^3\)\), this expression is simply one term, hence it is a monomial.

Key characteristics of a monomial include:
  • It contains only one term.
  • The term is a product based on variables, coefficients, and possibly constants (like \(7x^2\), \(-3\), or \(\frac{2}{3}a\)).
  • There are no additions or subtractions between different variables or terms, meaning it should always appear as a single "chunk."
Understanding these traits helps in classifying any polynomial expression that consists of just one term, as a monomial.
Binomial
A binomial is a type of polynomial consisting of exactly two terms. These terms are separated by either a plus (+) or minus (-) sign. Each term in a binomial can further involve variables raised to some power, coefficients, and constants as well. For instance, \(\(x + 1\)\), or \(\(3a^2 - 5\)\), are examples of binomials.

Some key traits of a binomial include:
  • It contains exactly two distinct terms.
  • Terms are separated by a plus or minus sign.
  • Each term can comprise variables, coefficients, and constants.
Binomials are frequently encountered in algebra, and recognizing these two-term polynomials is useful for various operations, including multiplication and factoring.
Trinomial
In algebra, a trinomial is a polynomial composed of three terms. Much like a binomial, the terms in a trinomial are linked by either addition (+) or subtraction (-). Consider expressions such as \(\(x^2 + 2x + 1\)\) or \(\(4a^2 - 3b + 2\)\), which are both examples of trinomials.

For identifying a trinomial, note these characteristics:
  • There are exactly three separate terms.
  • Each term is typically divided by plus or minus signs.
  • Involves a mix of variables, exponents, coefficients, and constants, spread across its three terms.
Recognizing a trinomial helps when you're performing algebraic operations, solving equations, or factoring polynomials into simpler expressions.

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

Perform the operations. $$-4\left(x^{2} y^{2}+x y^{3}+x y^{2} z\right)-2\left(x^{2} y^{2}-4 x y^{2} z\right)-2\left(8 x y^{3}-y\right)$$

Simplify. $$2(x+3)+4(x-2)$$

Perform the operations. $$\left(4 c^{2}+3 c-2\right)+\left(3 c^{2}+4 c+2\right)$$

Perform each division. If there is a remainder, leave the answer in quotient \(+\frac{\text { remainder }}{\text { divisor }}\) form. Assume no division by \(0 .\) $$\frac{x^{3}+3 x^{2}+3 x+1}{x+1}$$

Simplify or solve as appropriate. $$(b+2)(b-2)+2 b(b+1)$$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

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.