/*! 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 28 List the nonzero coefficients of... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 12: Problem 28

List the nonzero coefficients of the polynomials. $$ \pi x $$

Short Answer

Expert verified
Question: List the non-zero coefficients of the polynomial 蟺x. Answer: 蟺

Step by step solution

01

Identify the term in the polynomial

We have only one term in the polynomial, which is \(\pi x\).
02

Determine the coefficient

The coefficient of the term \(x\) is the number that is multiplied by the variable. In our case, the coefficient is \(\pi\).
03

List the non-zero coefficients

The only coefficient in the polynomial is \(\pi\), which is non-zero. Therefore, the list of non-zero coefficients consists of a single element: \(\pi\).

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
A polynomial is a mathematical expression made up of terms. Each term in a polynomial consists of a constant and a variable raised to a power, often summed or subtracted together. Here is how you recognize a polynomial:
  • It must consist of terms with variables and coefficients.
  • The exponents on the variables should be whole numbers (i.e., non-negative integers).
  • The operations involved must only include addition, subtraction, and multiplication.
For example, in the polynomial \(\pi x\), there is only one term. This makes it a single term polynomial, which means it fits the definition. Polynomials can also be categorized based on their degree, which is the highest exponent on the variable. A polynomial with a single term is also known as a monomial.
Coefficients
Coefficients are the numbers that multiply the variables within polynomial terms. They play a crucial role in defining the polynomial's characteristics.Let's break it down:
  • The coefficient is always paired with a variable.
  • In a polynomial such as \(\pi x\), \pi\ is the coefficient. It is not a whole number but instead a mathematical constant.
  • Coefficients can be positive, negative, or even zero, but when listing non-zero coefficients, zero is excluded.
Understanding the coefficient is key when you are working with polynomials, as it impacts the graph and the algebraic calculations of the polynomial.
Single Variable Polynomials
A single variable polynomial is a polynomial that includes only one variable. Each term in the polynomial consists of this variable raised to some power and multiplied by a coefficient.Here's what makes a polynomial a single variable type:
  • All terms must utilize the same variable.
  • There can be multiple terms, each with different powers of the variable but all involving the same one.
  • Examples include expressions like \(3x^2 + 2x + 1\) or our example of \(\pi x\) where \(x\) is the sole variable.
Single variable polynomials are often simpler to analyze as they involve operations in one dimension only. They form the foundation for understanding more complex polynomials involving multiple 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

For what values of \(a\) does the equation have a solution in \(x\) ? $$ \left(a x^{2}+1\right)(x-a)=0 $$

State the given quantities if \(p(x)\) is a polynomial of degree 5 with constant term 3 , and \(q(x)\) is a polynomial of degree 8 with constant term -2. The degree of \(p(x)^{3} q(x)^{2}\).

Refer to the functions \(f(x)\) and \(g(x),\) where the function $$ g(x)=1+\frac{1}{2} x+\frac{3}{8} x^{2}+\frac{5}{16} x^{3} $$ is used to approximate the values of $$ f(x)=\frac{1}{\sqrt{1-x}} $$ Show that \(f(x)\) is undefined at \(x=1\) and \(x=2\), but that \(g(x)\) is defined at these values. Explain why the algebraic operations used to define \(f\) may lead to undefined values, whereas the operations used to define \(g\) will not.

Give the leading term. $$ 13 x^{4}\left(2 x^{2}+1\right) $$

Without expanding, what is the constant term of $$ (x+2)(x+3)(x+4)(x+5)(x+6) ? $$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

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.