Final answer:
Using the Remainder Theorem, the remainder when f(x) = x^4 - 5x^3 - 5 is divided by x - 6 is calculated by plugging 6 into the function, yielding a remainder of 211.
Step-by-step explanation:
To find the remainder when the function f(x) = x^4 - 5x^3 - 5 is divided by x - 6, we can use the Remainder Theorem. According to the theorem, if a polynomial f(x) is divided by x - a, the remainder is f(a). Therefore, to find the remainder of f(x) divided by x - 6, we need to calculate f(6).
Substituting 6 into the function, we get:
f(6) = 6^4 - 5(6)^3 - 5
f(6) = 1296 - 5(216) - 5
f(6) = 1296 - 1080 - 5
f(6) = 216 - 5
f(6) = 211
Therefore, the remainder when f(x) is divided by x - 6 is 211.