Problem 15 How do you determine the degree ... [FREE SOLUTION]

Chapter 6: Problem 15

How do you determine the degree of a term in a polynomial in more than one variable?

Short Answer

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To determine the degree of a term in a polynomial with multiple variables, follow these steps: 1. Understand that the degree of a term is the sum of the exponents of all its variables. 2. Identify the multivariate terms in the polynomial (e.g., \(3x^2y^4\)). 3. Add the exponents of the variables in each term to find their degrees (e.g., in \(5x^3y^2\), the degree is \(3+2=5\)). 4. The degree of the entire polynomial is the highest degree among all its terms. For example, in the polynomial \(3x^2y^4 + 5x^3y^2 - 2x^4y\), the respective degrees of the terms are 6, 5, and 5, so the degree of the polynomial is 6.

Step by step solution

Understanding the concept of the degree of a term

To determine the degree of a term in a polynomial in more than one variable, we must first understand what the degree of a term means. A term's degree in a polynomial is the sum of the exponents of all its variables. For example, in \(x^2y^3\), the degree would be the sum of the exponents of \(x\) (which is 2) and \(y\) (which is 3), so the degree of the term is 5. Now that we understand the concept let's move to the next step.

Identifying the multivariate terms in the polynomial

We will now identify the terms in the polynomial containing more than one variable, which are called multivariate terms. An example of such a term is \(3x^2y^4\), where both variables x and y are raised to some powers.

Adding the exponents of the variables

To find the degree of each multivariate term, we will add the exponents of its variables. For example, if we have a term like \(5x^3y^2\), we will add the exponents of \(x\) (which is 3) and \(y\) (which is 2), yielding a degree of 5 for the term.

Applying the concept to the entire polynomial

After finding the degree of each multivariate term, we can apply the same concept to other terms in the polynomial. We must remember that the degree of the entire polynomial will be the highest degree of all of its terms. For example, in the polynomial \(3x^2y^4 + 5x^3y^2 - 2x^4y\), the respective degrees of the terms are 6, 5, and 5. Therefore, the degree of the whole polynomial is 6, which is the highest degree among all the terms. By following these steps, we can determine the degree of a term in a polynomial in more than one variable and assess the degree of the entire polynomial as well.

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91影视

How do you determine the degree of a term in a polynomial in more than one variable?

Short Answer

Step by step solution

Understanding the concept of the degree of a term

Identifying the multivariate terms in the polynomial

Adding the exponents of the variables

Applying the concept to the entire polynomial

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