/*! 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 102 Determine whether each statement... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 102

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. Adding polynomials in several variables is the same as adding like terms.

Short Answer

Expert verified
The statement 'Adding polynomials in several variables is the same as adding like terms' makes sense because the addition of polynomials, in essence, is the addition of like terms.

Step by step solution

01

Understanding of Polynomials

A polynomial is an algebraic expression that comprises variables (like x, y, z) and coefficients. An example of a polynomial with several variables is \(3x^2y^3z + 2xy - z^2\).
02

Identifying Like Terms

Like terms are the terms that have the same variables and exponents. The coefficients do not have to be the same. For instance, in the polynomial \(3x^2 + 5x^2\), \(3x^2\) and \(5x^2\) are like terms.
03

Adding Polynomials

To add polynomials, you need to add only the coefficients of like terms. The sum of the like terms \(3x^2 + 5x^2\) is \(8x^2\).
04

Conclusion and Reasoning

To conclude, the statement 'Adding polynomials in several variables is the same as adding like terms' is correct or 'makes sense'. This is because when a polynomial is being added, essentially the like terms are being added.

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!

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

Are the expressions $$ \frac{12 x^{2}+6 x}{3 x} \text { and } 4 x+2 $$ equal for every value of \(x ?\) Explain.

Will help you prepare for the material covered in the next section. In each exercise, find the indicated products. Then, if possible, state a fast method for finding these products. (You may already be familiar with some of these methods from a high school algebra course.) a. \((x+3)(x-3)\) b. \((x+5)(x-5)\)

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. If \(5^{-2}\) is raised to the third power, the result is a number between 0 and 1

We have seen that in \(2009,\) the United States government spent more than it had collected in taxes, resulting in a budget deficit of \(\$ 1.35\) trillion. The Washington Monument, overlooking the U.S. Capitol, stands about 555 feet tall. Stacked end to end, how many monuments would it take to reach 1.35 trillion feet? (Note: That's more than twice the distance from Earth to the sun.)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$5^{2} \cdot 5^{-2}>2^{5} \cdot 2^{-5}$$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Pure Maths

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.