Problem 52 Write each polynomial in descend... [FREE SOLUTION]

Chapter 3: Problem 52

Write each polynomial in descending order of degree. $$21 m-6 m^{7}+9 m^{2}+13-8 m^{5}$$

Short Answer

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Question: Rewrite the polynomial $$-6 m^7 + 21 m + 9 m^2 + 13 - 8 m^5$$ in descending order of degree. Answer: $$-6 m^7 - 8 m^5 + 9 m^2 + 21 m + 13$$

Step by step solution

Identify the terms of the polynomial

Identify each individual term of the original polynomial: $$-6 m^{7}, 21 m, 9 m^{2}, 13, -8 m^{5}$$

Order the terms by descending degree

Rearrange these terms based on descending degree: $$-6 m^{7}, -8 m^{5}, 9 m^{2}, 21 m, 13$$

Write the final polynomial

Write the terms in the correct order to form the final polynomial in descending order of degree: $$-6 m^{7}-8 m^{5}+9 m^{2}+21 m+13$$

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Polynomial Terms

Understanding polynomial terms is essential for anyone exploring algebra. A polynomial is like a mathematical phrase composed of 'words' called terms. Each term is either a number, a variable (like m), or a product of numbers and variables combined with an operation (multiplication).

For instance, in the polynomial 21m - 6m⁷ + 9m² + 13 - 8m⁵, the terms are -6m⁷, 21m, 9m², 13, and -8m⁵. It's important to identify these terms correctly because each one represents a vital piece of the polynomial puzzle.

Degree of a Polynomial

The degree of a polynomial is determined by the term with the highest exponent. This is the 'level' of the polynomial and gives us vital information about its behaviour, particularly its graph. In the polynomial -6m⁷ - 8m⁵ + 9m² + 21m + 13, the term with the highest exponent is -6m⁷, which has an exponent of 7. Hence, we say that the degree of this polynomial is 7.

Knowing the degree is also useful because it tells us the maximum number of roots or solutions to the polynomial equation, as well as the most extreme changes in direction of its graph, which are called its turning points.

Rearranging Polynomial Terms

Rearranging polynomial terms in descending order of degree means starting with the highest degree term and working down to the constant, or the term without a variable. This organization can help in finding the solution of polynomial equations, simplifying expressions, and analyzing graphs.

By rearranging the terms of -6m⁷ + 21m + 9m² + 13 - 8m⁵ to -6m⁷ - 8m⁵ + 9m² + 21m + 13, we align the terms in a way that clearly displays the relative 'weight' of each term within the polynomial. This practice makes it easier to use polynomial in various applications such as solving equations and plotting graphs.

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91影视

Write each polynomial in descending order of degree. $$21 m-6 m^{7}+9 m^{2}+13-8 m^{5}$$

Short Answer

Step by step solution

Identify the terms of the polynomial

Order the terms by descending degree

Write the final polynomial

Key Concepts

Polynomial Terms

Degree of a Polynomial

Rearranging Polynomial Terms

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