Respuesta :

gmany

If the polynomial degree is 3, then the largest power with the variable(s) is 3.

We have:

[tex]10x^2+2x^my-4y\\\Downarrow\\10x^2-2nd\ degree\\\\2x^my-(m+1)th\ degree\\\\-4y-1st\ degree[/tex]

Therefore m +1 = 3 → m = 2

Answer: 2

facundo3141592

We want to find the value of an exponent given that we know the degree of the polynomial.

We will see that m = 2.

The degree of a polynomial is given by the maximum exponent of the polynomial. If the polynomial is multivariable, the degree is given by the maximum sum of exponents in the same term.

Here we have the polynomial:

[tex]10*x^2 + 2*x^m*y + 4*y[/tex]

We know that the degree is 3, notice that the maximum sum of exponents comes from the second term, then we must solve:

m + 1  = 3

m = 3 - 1 = 2

m = 2

Then the polynomial is:

[tex]10*x^2 + 2*x^2*y - 4*y[/tex]

If you want to learn more, you can read:

https://brainly.com/question/2284746

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