Final answer:
By applying the Remainder Theorem, we find that when x = -3 is substituted into the polynomial, the value of b that would yield a remainder of -5 does not match any of the provided options. The actual value of b is 10, indicating a potential error in the question or the options provided.
The actual value of b is 10
Step-by-step explanation:
To find the value of b when the polynomial 2x^3 + 11x^2 + bx - 20 is divided by (x + 3) and the remainder is -5, we can use the Remainder Theorem. According to this theorem, if a polynomial f(x) is divided by (x - r), the remainder is f(r). In this case, we have r = -3.
We need to substitute x = -3 into the polynomial and set it equal to -5:
2(-3)^3 + 11(-3)^2 + b(-3) - 20 = -5
Simplifying this, we get:
-54 + 99 - 3b - 20 = -5
Then:
-3b + 25 = -5
Now solve for b
-3b = -30
b = 10
However, none of the provided options (A: b = 29, B: b = 28, C: b = 27, D: b = 26) match the correct value of b. Therefore, there must be a mistake either in the calculation or in the provided options.