What is the total degree of x^6y^3z^4 + 4x^2y^2z^9 − 12?

Correct answer: 13

For a polynomial in several variables, the total degree of a term is the sum of the exponents of all variables in that term. The first term x^6y^3z^4 has total degree 6 + 3 + 4 = 13. The second term 4x^2y^2z^9 has total degree 2 + 2 + 9 = 13; its numerical coefficient 4 does not affect degree. The constant term −12 has degree 0. The degree of the polynomial is the largest term degree, so it is 13. Therefore option A is correct. Adding the exponents across a term is essential; taking only the largest exponent would incorrectly suggest 9 or 6, and ignoring the first term would miss the maximum.