Question

Write each polynomial in descending order of the variable $x$. If the polynomial is already in descending order, so state. Give the degree of each polynomial.$-5+2 x-x^{2}$

Name: Problem 17, Chapter 5: Intermediate Algebra for College Students
Uploaded: 2020-05-08T16:19:12-08:00
Duration: 49 s
Channel: Ramzi Deek
Description: Write each polynomial in descending order of the variable x. If the polynomial is already in descending order, so state. Give the degree of each polynomial.-5+2 x-x^2

   Write each polynomial in descending order of the variable $x$. If the polynomial is already in descending order, so state. Give the degree of each polynomial.$-5+2 x-x^{2}$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 5, Problem 17

Instant Answer

Solved by Expert Ramzi Deek

05/08/2020

Step 1

To do this, we rearrange the terms from the highest power of $x$ to the lowest power of $x$. So, we rewrite the polynomial as $-x^2 + 2x - 5$. Now, we need to find the degree of the polynomial. The degree of a polynomial is the highest power of the variable Show more…

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Write each polynomial in descending order of the variable $x$. If the polynomial is already in descending order, so state. Give the degree of each polynomial.$-5+2 x-x^{2}$

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Key Concepts

Polynomial

A polynomial is an algebraic expression composed of variables, coefficients, and non-negative integer exponents, combined using operations such as addition, subtraction, and multiplication. It forms the basis for various operations and analyses in algebra and calculus.

Standard Form

Writing a polynomial in standard form means arranging its terms in order from the highest exponent to the lowest exponent. This descending order makes it easier to identify properties of the polynomial, compare polynomials, and perform functions like polynomial division and factorization.

Degree of a Polynomial

The degree of a polynomial is the highest exponent on the variable among all the terms, provided the corresponding coefficient is not zero. This concept is critical because the degree provides insight into the polynomial's behavior, including its end behavior and the maximum number of roots it can have.

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