Math Problem Statement

The degree of the polynomial is 3. What is the value of m?

Solution

To find the value of mm for which the degree of the polynomial is 3, let's analyze the polynomial given in the image:

10x2+2xmy4y10x^2 + 2x^m y - 4y

Degree of the Polynomial

The degree of a polynomial is determined by the highest sum of the exponents in any single term.

  1. First term: 10x210x^2 has a degree of 22 (since 2+0=22 + 0 = 2).
  2. Second term: 2xmy2x^m y has a degree of m+1m + 1 (since the exponent of xx is mm and the exponent of yy is 11).
  3. Third term: 4y-4y has a degree of 11 (since the exponent of yy is 11).

Since the degree of the polynomial is given as 33, the term with the highest degree must equal 3. The highest degree is from the term 2xmy2x^m y, which is m+1m + 1.

Equation:

m+1=3m + 1 = 3

Solving for mm:

m=31=2m = 3 - 1 = 2

Thus, the value of mm is 2\boxed{2}.

Would you like further details or have any questions?

Related Questions:

  1. What happens to the degree if mm is greater than 2?
  2. How does the presence of yy affect the degree of each term?
  3. What is the degree of the polynomial if mm is less than 2?
  4. How do coefficients affect the degree of a polynomial?
  5. Can you find a value of mm that would make the polynomial's degree equal to 4?

Tip:

Always remember that the degree of a polynomial is determined by the term with the highest sum of exponents, not just the highest exponent of a single variable.