/*! 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 Identify the terms of each polyn... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 18

Identify the terms of each polynomial. \(n^{5}-4 n^{3}+2 n-8\)

Short Answer

Expert verified
The terms are \( n^{5} \), \( -4n^{3} \), \( 2n \), and \( -8 \).

Step by step solution

01

Understand the Polynomial Expression

Read the entire polynomial expression carefully: \( n^{5} - 4n^{3} + 2n - 8 \).
02

Identify the Terms

A term in a polynomial is any product of numbers and variables that are separated by a plus (+) or minus (鈭�) sign. Identify each term from the expression: 1. \( n^{5} \)2. \( -4n^{3} \)3. \( 2n \)4. \( -8 \).
03

List Each Term

Write down each term identified in the previous step:1. \( n^{5} \)2. \( -4n^{3} \)3. \( 2n \)4. \( -8 \).

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.

Polynomial Expression
A polynomial expression is a mathematical expression that involves a sum of powers in one or more variables, with constant coefficients. In simple terms, it's like a series of terms where some combination of numbers and variables are added or subtracted.
For example, in the polynomial expression {5 - 4n{3 + 2n - 8}, each term is separated by a plus (+) or minus (鈭�) sign.
Understanding polynomial expressions is crucial for solving many algebra problems. They are used in various areas of mathematics, including calculus and real-world applications.
Identifying Terms
The terms of a polynomial are individual components separated by plus (+) or minus (鈭�) signs.
For instance, in the polynomial {}5 - 4n{3 + 2n - 8ot every distinct part separated by those signs is a term. Identifying each term is important. Here's how you can do it:
1. Look for each section of the expression separated by + or - signs.
2. Be careful to include any negative signs with the relevant term.
3. Write down each distinct entity you identified as a term.
So, in {}5 - 4n{3 + 2n - 8ot only are the terms 5, -4n{3, 2n, and -8.
Variables and Constants
Polynomials consist of both variables and constants. Understanding the difference is key.
Variables are symbols that represent numbers and can change value. For example, in the term ^5ot is the variable.
Constants are fixed values that do not change. For example, in -8, the number 8 is a constant.
By distinguishing variables and constants in a polynomial, you can better understand how the expression behaves under different conditions and solve related problems more efficiently.
Algebraic Expressions
An algebraic expression is a mathematical phrase that can include numbers, variables, and operations (like addition and multiplication).
Polynomials are a specific type of algebraic expression. They feature sums of variables raised to whole number powers, multiplied by coefficients, and separated by plus or minus signs.
For example, the expression }}5 - 4n{3 + 2n - 8ot is an algebraic expression that takes the specific form of a polynomial.
Mastering algebraic expressions forms the foundation for understanding more complicated math concepts, making it easier to solve equations and understand functional relationships between numbers and variables.

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

Yearly Depreciation. An investment \(P\) that drops in value at the yearly rate \(r\) drops in value to $$ P(1-r)^{t} $$ after \(t\) years. Find a polynomial that can be used to determine the value to which \(P\) has dropped after 2 years.

Computer spreadsheet applications allow values for cells in a spreadsheet to be calculated from values in other cells. For example, if the cell Cl contains the formula $$ =\mathrm{A} 1+2 * \mathrm{B} 1 $$ the value in Cl will be the sum of the value in Al and twice the value in B1. This formula is a polynomial in the two variables Al and B1. The cell D4 contains the formula $$ =2 * \mathrm{A} 4+3 * \mathrm{B} 4 $$ What is the value in \(\mathrm{D} 4\) if the value in \(\mathrm{A} 4\) is 5 and the value in \(\mathrm{B} 4\) is \(10^{2}?\)

Solve for \(x: \frac{t^{26}}{t^{x}}=t^{x}\).

To prepare for Section \(5.2,\) review operations with integers (Sections \(1.5-1.7)\) Perform the indicated operations. $$ -8(-10) $$

To prepare for Section 5.3, review combining like terms and evaluating expressions (Sections 1.6 and 1.8). Combine like terms. $$ -3 x+(-2)-5-(-x) $$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Probability and 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.