Final answer:
A polynomial with the only zero at 8 with a multiplicity of 6 is written as (x - 8)^6. The degree of this polynomial is 6. Thus, the degree of the polynomial f(x) is 6.
Step-by-step explanation:
To write a polynomial whose only zero is 8 with a multiplicity of 6, you need to consider that the multiplicity of a root refers to the number of times that root appears as a zero of the function.
Since 8 is the only zero and it has a multiplicity of 6, the polynomial will have the factor (x - 8) raised to the power of 6. Therefore, the polynomial can be written as:
f(x) = (x - 8)^6.
The degree of this polynomial is equal to the sum of the multiplicities of its zeros, which in this case is just the multiplicity of the single zero, 8.
Thus, the degree of the polynomial f(x) is 6.