/*! 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 90 In the following exercises, list... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 90

In the following exercises, list the terms in the given expression. $$11 x^{2}+8 x+5$$

Short Answer

Expert verified
The terms are \(11x^{2}\), \(8x\), and \(5\).

Step by step solution

01

Identify the expression

The given expression is \(11x^{2} + 8x + 5\). Recognize that it is a polynomial in the variable \(x\).
02

Break down the expression into terms

A term in an algebraic expression is a single mathematical expression. In \(11x^{2} + 8x + 5\), each part separated by a plus (\(+\)) sign is a term.
03

List the terms

The terms in the expression \(11x^{2} + 8x + 5\) are: \(11x^{2}\), \(8x\), and \(5\).

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.

Algebraic Expressions
Understanding algebraic expressions is key in the realm of algebra. An algebraic expression is a combination of numbers, variables, and arithmetic operations (like addition or multiplication). For example, in the expression 11虫虏 + 8x + 5, you have numbers (11, 8, 5), the variable x, and the operations of addition and multiplication. To grasp this better, remember the following:
  • Numbers within the expression are called constants.
  • Variables are symbols that can represent different values.
  • Operations denote how these numbers and variables interact with each other.
Algebraic expressions help us to write complex mathematical ideas concisely and solve equations to find an unknown variable's value.
Polynomial
Let's explore a specific type of algebraic expression - the polynomial. A polynomial is an expression made up of multiple terms, where each term includes a variable raised to a non-negative integer exponent. Consider the polynomial provided in the exercise: 11虫虏 + 8x + 5. It's a polynomial in the variable x. Here is why:
  • Each term follows the form ax^n, where a is a constant coefficient and n is a non-negative integer.
  • This particular polynomial has three terms.
  • Polynomials can be classified by their degree (the highest exponent). In our polynomial, the highest degree is 2 (coming from 11虫虏).
Polynomials are foundational in algebra because many algebraic operations, functions, and equations are built upon them.
Terms in Polynomial
Understanding the terms in a polynomial is crucial for solving problems. A term is a single standalone mathematical expression within a polynomial. It can include a coefficient (a number), a variable, and an exponent. In the polynomial 11虫虏 + 8x + 5, let's break down each term:
  • 11虫虏: This term has a coefficient of 11 and a variable x raised to the power of 2.
  • 8x: Here, the coefficient is 8, and the variable x is to the power of 1 (though we don鈥檛 always write the 1).
  • 5: This is a constant term without any variable.
Remember, identifying and understanding each term allows us to perform operations like addition, subtraction, and multiplication on polynomials easily. Recognizing the structure of these terms will help simplify and solve complex algebraic equations.

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

In the following exercises, solve each equation. $$ n-6=25 $$

Sale purchase Rita bought a sofa that was on sale for \(\$ 1299 .\) She paid a total of \(\$ 1409,\) including sales tax. Find the amount of the sales tax, \(t,\) by solving the equation \(1299+t=1409\)

Sale purchase Arthur bought a suit that was on sale for \(\$ 120\) off. He paid \(\$ 340\) for the suit. Find the original price, \(p,\) of the suit by solving the equation \(p-120=340\)

In the following exercises, translate the given sentence into an algebraic equation and then solve it. The difference of d and 30 is equal to 52.

In the following exercises, solve each equation using the subtraction property of equality. $$ 16=x+9 $$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

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.