the degree of the polynomial $10x^{2}+2x^{m}y - 4y$ is 3. what is the value of $m$?\n1\n2\n3\n4

Explanation:

Step1: Recall degree - of - polynomial rule

The degree of a term in a polynomial in two variables (x) and (y) is the sum of the exponents of (x) and (y) in that term. The degree of the polynomial is the highest degree of its terms. The degree of the term (10x^{2}) is (2), the degree of the term (2x^{m}y) is (m + 1), and the degree of the term (-4y) is (1).

Step2: Set up equation based on given degree

Since the degree of the polynomial (10x^{2}+2x^{m}y - 4y) is (3), and the highest - degree term must have a degree of (3). The term (2x^{m}y) must be the highest - degree term. So we set up the equation (m + 1=3).

Step3: Solve the equation for (m)

Subtract (1) from both sides of the equation (m + 1=3). We get (m=3 - 1). So (m = 2).

Answer:

2