/*! 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 113 Explain how to subtract polynomi... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 113

Explain how to subtract polynomials.

Short Answer

Expert verified
The process of subtracting polynomials involves rewriting the polynomials with like terms aligned, then subtracting the coefficients of like terms. Remember to change the signs of all terms in the polynomial being subtracted. Our example results in the polynomial \(-x^2 + x - 1\).

Step by step solution

01

Understand Polynomials

A polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variables. For example, \(3x^2 - 2x + 1\) is a polynomial.
02

Arrange Polynomial Terms

If the terms of the polynomials are not already arranged in descending order by degree, they should be rearranged this way. This makes the subtraction process easier as like terms are in the same position in both polynomials.
03

Align Like Terms

Write the polynomials vertically in such a way that the like terms (terms that have the same variable raised to the same power) are under each other. For example, if subtracting \(4x^2 - 3x + 2\) from \(3x^2 - 2x + 1\), the setup should look like this: \[3x^2 - 2x + 1\] - \[4x^2 - 3x + 2\]
04

Subtract Like Terms from Each Polynomial

Subtract the coefficient (numerical part) of each term in the second polynomial from the corresponding term in the first polynomial. Remember that you are subtracting the entire term, so the sign of the term changes in the subtraction. For example, using our previous polynomials, after subtracting, we will have \[-x^2 + x - 1\].
05

Write the Result

The result should be written clearly, still preserving the descending order by degree. Based on the previous example, the result would be written as \(-x^2 + x - 1\).

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

Solve the system: $$\left\\{\begin{array}{l}7 x-6 y=17 \\\3 x+y=18\end{array}\right.$$ (Section 4.3, Example 2)

Explain how to divide a polynomial that is not a monomial by a monomial. Give an example.

determine whether each statement 鈥渕akes sense鈥� or 鈥渄oes not make sense鈥� and explain your reasoning. As long as I understand how to add and subtract polynomials, I can select the format, horizontal or vertical, that works best for me.

In your own words, explain how to divide a polynomial by a binomial. Use \(\frac{x^{2}+4}{x+2}\) in your explanation.

Find the absolute value: \(|-20.3|\)
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Mechanics 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.