If 2x + 1 is a factor of 2x² + ax - 3, find the value of a.

2x + 1 = 0 ⇒ x = $-\dfrac{1}{2}$

Since, 2x + 1 is a factor of 2x² + ax - 3

∴ On substituting x = $-\dfrac{1}{2}$ in 2x² + ax - 3 remainder = 0.

$\Rightarrow 2\Big(-\dfrac{1}{2}\Big)^2 + a\Big(-\dfrac{1}{2}\Big) - 3 = 0 \\[1em] \Rightarrow 2 \times \dfrac{1}{4} - \dfrac{a}{2} - 3 = 0 \\[1em] \Rightarrow \dfrac{1}{2} - \dfrac{a}{2} = 3 \\[1em] \Rightarrow \dfrac{1 - a}{2} = 3 \\[1em] \Rightarrow 1 - a = 6 \\[1em] \Rightarrow a = 1 - 6 = -5.$

Hence, a = -5.