write the degree of following polynomials. (i) 2xsquare+3xy+5ysqaure+2

Identify Terms Degree: Identify the highest power of the variable(s) in each term of the polynomial. The polynomial is 2x^2 + 3xy + 5y^2 + 2. We need to look at each term to determine its degree. - The term 2x^2 has a degree of 2 (since x is raised to the power of 2). - 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 1 + 1 = 2. - The term 5y^2 has a degree of 2 (since y is raised to the power of 2). - The term 2 is a constant and has a degree of 0.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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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 $2$ .