Final answer:
The remainder when p(x) = x⁴ - 2x³ - 6x² + 3 is divided by x - 2 is -18, calculated using the remainder theorem by evaluating p(2). However, this result does not match any of the provided options.
Step-by-step explanation:
The remainder when p(x) = x⁴ - 2x³ - 6x² + 3 is divided by x - 2 can be found using synthetic division or by evaluating p(2) directly. Since we are looking for a remainder, we'll use the remainder theorem which states that the remainder when a polynomial p(x) is divided by x - k is simply p(k).
Evaluating p(2), we substitute x with 2:
p(2) = 2⁴ - 2(2³) - 6(2²) + 3
= 16 - 2(8) - 6(4) + 3
= 16 - 16 - 24 + 3
= -21 + 3
= -18
Therefore, the remainder is -18, none of the provided options A) 7 B) 11 C) -5 D) 27 match. It seems there might be an error in the options given.