Question

Give a) the degree of each polynomial and b) its leading coefficient.$3 c^{5} d^{2}-5 c^{4} d^{4}+2 c^{2} d^{5}$

Name: Problem 28, Chapter 5: Intermediate Algebra for College Students
Uploaded: 2020-07-17T09:20:46-08:00
Duration: 46 s
Channel: Ankit Gupta
Description: Give a) the degree of each polynomial and b) its leading coefficient.3 c^5 d^2-5 c^4 d^4+2 c^2 d^5

   Give a) the degree of each polynomial and b) its leading coefficient.$3 c^{5} d^{2}-5 c^{4} d^{4}+2 c^{2} d^{5}$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 5, Problem 28

Instant Answer

Solved by Expert Ankit Gupta

07/17/2020

Step 1

1) $3c^5d^2$: The degree of this term is the sum of the exponents of the variables, which is $5+2=7$. 2) $-5c^4d^4$: The degree of this term is the sum of the exponents of the variables, which is $4+4=8$. 3) $2c^2d^5$: The degree of this term is the sum of the Show more…

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Give a) the degree of each polynomial and b) its leading coefficient.$3 c^{5} d^{2}-5 c^{4} d^{4}+2 c^{2} d^{5}$

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Key Concepts

Total Degree of a Polynomial

In the context of polynomials with more than one variable, the total degree of a term is calculated by adding the exponents of all variables in that term. The degree of the polynomial is then the highest total degree found among its terms. This concept helps determine the 'size' or 'order' of the polynomial and is essential in understanding its behavior and the complexity of its expression.

Leading Coefficient

The leading coefficient of a polynomial is the coefficient of the term that is considered the 'largest' according to a specified ordering, often based on the total degree of the term. In many cases, especially with a graded lexicographic order, the term with the highest total degree determines the leading coefficient. This coefficient plays a key role in characterizing the polynomial's behavior, particularly for large variable values and in polynomial division or factorization.

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