The degree of a polynomial with different variables is determined by the highest sum of the exponents of the variables in any one term of the polynomial.
To elaborate: When a polynomial contains multiple variables, the degree of each term is found by adding the exponents of those variables within that term. The degree of the entire polynomial is then the highest degree among all its terms.
Here's a breakdown:
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Degree of a Term: For a single term containing multiple variables, sum the exponents of all the variables. For instance, in the term
3x²y³z, the degree is 2 + 3 + 1 = 6 (sincezis implicitlyz¹). -
Degree of the Polynomial: The degree of the whole polynomial is the largest degree found among all its individual terms.
Examples:
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Polynomial:
5x² + 3xy + 2y- Degree of
5x²: 2 - Degree of
3xy: 1 + 1 = 2 - Degree of
2y: 1 - Therefore, the degree of the polynomial is 2.
- Degree of
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Polynomial:
7x³y² - 4x²yz + 9z⁴ - 2- Degree of
7x³y²: 3 + 2 = 5 - Degree of
-4x²yz: 2 + 1 + 1 = 4 - Degree of
9z⁴: 4 - Degree of
-2: 0 (Constant term) - Therefore, the degree of the polynomial is 5.
- Degree of
-
Polynomial:
x + y + z- Degree of
x: 1 - Degree of
y: 1 - Degree of
z: 1 - Therefore, the degree of the polynomial is 1.
- Degree of
In summary, identify the term with the highest sum of exponents on its variables; that sum is the degree of the polynomial.
