Final answer:
The degree of the polynomial -x⁶u - 6 - 4u³y²x³ - 2y⁶ is 8, as the term with the highest combined powers of its variables is -4u³y²x³.
Step-by-step explanation:
The student has asked for calculating the degree of the polynomial -x⁶u - 6 - 4u³y²x³ - 2y⁶. The degree of a polynomial is the highest power of the variable in any term of the polynomial.
To find the degree, we look at each term separately:
- The term -x⁶u has a degree of 7 (x raised to the power of 6 and u raised to the power of 1).
- The constant term -6 has a degree of 0.
- The term -4u³y²x³ combines x, y, and u with respective powers 3, 2, and 3. When combined, the total degree is 3 + 2 + 3 = 8.
- The term -2y⁶ has a degree of 6 (y raised to the power of 6).
Among all the terms, the term with the highest degree is -4u³y²x³ which is of degree 8. Therefore, the degree of the entire polynomial is 8.