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write the degree of following polynomials. $(i) 2x^2+3xy+5y^2+2$

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Determine end behavior of polynomial and rational functions

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Q. write the degree of following polynomials.

(i) 2x^2+3xy+5y^2+2

Identify Terms Degree: Identify the highest power of the variable(s) in each term of the polynomial. $\newline$ The polynomial is $2x^2 + 3xy + 5y^2 + 2$ . We need to look at each term to determine its degree. $\newline$ - The term $2x^2$ has a degree of $2$ (since $x$ is raised to the power of $2$ ). $\newline$ - The term $3xy$ is a product of two variables, $x$ and $y$ , each raised to the power of $1$ . When multiplied, their degrees add up, so the degree of $3xy$ is $2x^2$ $0$ . $\newline$ - The term $2x^2$ $1$ has a degree of $2$ (since $y$ is raised to the power of $2$ ). $\newline$ - The term $2$ is a constant and has a degree of $2x^2$ $6$ .
Determine Polynomial Degree: Determine the degree of the polynomial. The degree of the polynomial is the highest degree of any term in the polynomial. From Step $1$ , we see that the highest degree among the terms is $2$ .
Conclude Polynomial Degree: Conclude the degree of the polynomial. Since the highest degree of any term in the polynomial $2x^2 + 3xy + 5y^2 + 2$ is $2$ , the degree of the polynomial is $2$ .

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