What is the total degree of (x^4y^2z^3+5x^2yz^6-8)?

Correct answer: (9)

For a polynomial in several variables, the total degree of a term is found by adding the exponents of all variables in that term. The degree of the whole polynomial is the greatest total degree among its nonzero terms. A constant such as \(-8\) has degree 0 and cannot exceed the degrees of the variable terms here.

For \(x^4y^2z^3\), the total degree is \(4+2+3=9\). For \(5x^2yz^6\), the exponent of y is 1, so its total degree is \(2+1+6=9\). The constant has degree 0. The greatest total degree is therefore 9, making option C correct. One must add exponents within a term, not choose only the largest individual exponent.