/*! 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 18 Write the following polynomials ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 18

Write the following polynomials in standard form. $$ 5 x 2-1-3 x+2 x 3 $$

Short Answer

Expert verified
The polynomial in standard form is \(2x^3 + 5x^2 - 3x - 1\).

Step by step solution

01

Rearrange the Terms

First, rearrange the terms of the polynomial to group all the terms with similar variable powers together. So, the polynomial is reordered as:\[2x^3 + 5x^2 - 3x - 1\]
02

Identify the Highest Degree Term

Next, identify the highest degree term in the polynomial, which dictates the leading term in standard form. Here, the highest degree is 3, corresponding to the term:\[2x^3\]
03

Write in Descending Order

Write the polynomial in descending order according to the degree of each term. Starting with the highest degree term, arrange them as:\[2x^3 + 5x^2 - 3x - 1\]
04

Verify Standard Form

Ensure that the polynomial is correctly written in standard form, where the terms are ordered from the highest degree to the lowest degree.\[2x^3 + 5x^2 - 3x - 1\] is indeed the standard form.

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.

Standard Form of Polynomials
Writing a polynomial in standard form means arranging its terms in a specific order. The standard form requires that each term is ordered from the highest to the lowest degree. This helps in simplifying calculations and makes it easier to identify key properties of the polynomial.
To put a polynomial in standard form, follow these steps:
  • Identify each term in the polynomial.
  • Arrange them from the highest power to the lowest power of the variable.
  • Combine any like terms if necessary.
For example, consider the polynomial \(2x^3 + 5x^2 - 3x - 1\). It is already in standard form because the degrees are listed from 3, 2, 1, to 0, respectively.
Degree of a Polynomial
The degree of a polynomial is a key aspect that tells us the highest power of the variable in the polynomial. This single number captures the complexity and behavior of the polynomial, especially as the variable grows large.
Identifying the degree of a polynomial involves:
  • Looking for the term with the highest exponent.
  • This exponent is the degree of the polynomial.
  • For multivariable polynomials, add the exponents in each term and find the maximum sum.
In the polynomial \(2x^3 + 5x^2 - 3x - 1\), the term \(2x^3\) has the highest power, meaning the degree of this polynomial is 3.
Descending Order of Terms
When ordering terms in a polynomial, we often arrange them in descending order based on the degree. This approach makes comparison easier and keeps the polynomial well-organized.
Here鈥檚 how you can organize a polynomial in descending order:
  • Identify the degree of each term.
  • Arrange the terms in decreasing order of their degrees.
  • Ensure that all terms with the same degree are combined or listed as one.
In the example \(2x^3 + 5x^2 - 3x - 1\), the terms are organized starting from the highest power, 3, then 2, followed by 1, and finally the constant term with degree 0. This descending order provides clarity and consistency.

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

Simplify. (Assume variables are nonzero.) $$ -30 \cdot(-2) 2 \cdot(-3) 0 $$

Simplify. $$ 12-3 $$

Simplify. $$ -10 a 2 b 3 \cdot 2 a-8 b-10 $$

Simplify. $$ (x 2 y-1)-4 $$

The value in dollars of a new MP3 player can be estimated by using the formula \(V=100(t+1)-1,\) where \(t\) is the number of years after purchase. How much was the MP3 player worth new?
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Statistics

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.