Solution:
The question asks for the remainder when the polynomial $$-x^3 + x^2 + 5x - 6$$ is divided by the binomial $$x + 3$$. To find the remainder without performing the entire polynomial long division, we can use the Remainder Theorem. According to the Remainder Theorem, if a polynomial $$f(x)$$ is divided by $$x - a$$, the remainder is $$f(a)$$.Since we're dividing by $$x + 3$$, we can apply the Remainder Theorem by substituting $$x = -3$$ into the polynomial:$$f(-3) = -(-3)^3 + (-3)^2 + 5(-3) - 6 $$$$f(-3) = -(-27) + 9 - 15 - 6$$$$f(-3) = 27 + 9 - 15 - 6$$$$f(-3) = 36 - 21$$$$f(-3) = 15$$So the remainder is 15, which corresponds to option B.