Final answer:
After substituting x = -5 into the polynomial P(x), which should yield zero if x + 5 is a factor, it is found that k must be equal to 6. However, this value is not an option provided in the question, indicating a possible error in the given choices.
Step-by-step explanation:
If x + 5 is a factor of P(x) = 3x^3 + 17x^2 + kx - 20, then by setting x = -5 and substituting it into the polynomial we should get zero, because for a value x = a to be a root of the polynomial, P(a) must be equal to zero. Performing the substitution:
- P(-5) = 3(-5)^3 + 17(-5)^2 + k(-5) - 20 = 0
-375 + 425 - 5k - 20 = 0
-375 + 425 - 20 = 5k
- 30 = 5k
- k = 6
Therefore, the value of k is not listed in the options given in the question. There seems to be a mistake since none of the given choices for k are correct based on the calculations.