Let the quotient be f(x) when $$5x^{4} —3x^{3} + 2x^{2} — 1$$ is divided by $$x^{2} + 4$$, the remainder be g(x) when $$2x^{3} — x + 1$$ with $$x^{2} + x + 1$$. The remainder when f(x) is divisible by g(x)

When $$5x^4-3x^3+2x^2-1\ $$ is divided by $$x^2+4$$, the quotient is $$5x^2-3x-18$$ and the remainder is $$12x+71$$
Here we are asked to take the quotient as f(x);
f(x) = $$5x^2-3x-18$$

When $$2x^3-x+1$$ is divided by $$x^2+x+1$$ the quotient is $$2x-2$$ and the remainder is $$-x+3$$
Here we are asked to take the remainder as g(x);
g(x) = $$-x+3$$

We are to find the remainder when f(x) is divided by g(x)
Upon dividing we would get the quotient as -5x-12 and the remainder is 18. 

Hence, Option B is thee correct answer.