When 2x³ - x² - 3x + 5 is divided by 2x + 1, then the remainder is

1. 6
2. -6
3. -3
4. 0

By remainder theorem, on dividing f(x) by (x - a), the remainder left is f(a).

f(x) = 2x³ - x² - 3x + 5

∴ On dividing f(x) by 2x + 1 or $2(x - \big(-\dfrac{1}{2}\big))$, Remainder = f$\big(-\dfrac{1}{2}\big)$

$f\big(-\dfrac{1}{2}\big) = 2\big(-\dfrac{1}{2}\big)^3 - \big(-\dfrac{1}{2}\big)^2 - 3\big(-\dfrac{1}{2}\big) + 5 \\[1em] = 2\big(-\dfrac{1}{8}\big) - \dfrac{1}{4} + \dfrac{3}{2} + 5 \\[1em] = -\dfrac{1}{4} - \dfrac{1}{4} + \dfrac{3}{2} + 5 \\[1em] = \dfrac{-1 -1 + 6 + 20}{4} \\[1em] = \dfrac{24}{4} \\[1em] = 6$

∴ Option 1, is the correct option.