Degree of polynomial 2x²y² + x²y² + 8x is:

The correct answer is 4. The degree of a polynomial is determined by the highest sum of the exponents of the variables in any single term of the polynomial. First, it's good practice to combine like terms if any exist. In the given polynomial 2x²y² + x²y² + 8x:

• Combine the like terms: 2x²y² + x²y² = 3x²y².
• The simplified polynomial becomes: 3x²y² + 8x.

Now, let's find the sum of the exponents for the variables in each term:

• For the term 3x²y², the exponents of the variables x and y are 2 and 2, respectively. The sum of these exponents is 2 + 2 = 4.
• For the term 8x, the exponent of the variable x is 1 (since x is x¹). The sum of exponents is 1.

Comparing the sums, the highest sum of exponents is 4. Therefore, the degree of the polynomial is 4.

• Option A, 2, is incorrect. While 2 is an exponent in the first term, it is not the sum of all exponents in that term, nor the highest degree of the polynomial.
• Option C, 7, is incorrect. This might result from incorrectly adding all the exponents in the first term (2+2) and the second term (1) or a misunderstanding of how to combine terms.
• Option D, 12, is incorrect. This value is likely obtained by an erroneous calculation, possibly by multiplying or adding numbers indiscriminately rather than following the rule for determining polynomial degree.