determine a real number so that the polynomial P(x)=2ax³-4x+ax-2a is divisible by x-2 and the remainder is -8

Since the given polynomial is divisible by x-2 and the remainder is -8. Using the remainder Theorem, we have: $$P(2)=-8$$ $$2a(2)^3-4(2)+a(2)-2a=-8$$ $$16a-8=-8$$ $$16a=0$$ $$a=0$$ The required answer is: $$a=0$$