If (2x + 1) is a factor of 6x³ + 5x² + ax - 2, find the value of a.

f(x) = 6x³ + 5x² + ax - 2

If, (2x + 1) or 2(x - (-$\dfrac{1}{2}$)) is a factor of f(x) then f(-$\dfrac{1}{2}$) = 0

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

On taking L.C.M.,

$\Rightarrow \dfrac{-3 + 5 - 2a - 8}{4} = 0 \\[0.5em] \Rightarrow \dfrac{-6 - 2a}{4} = 0 \\[0.5em]$

On Cross Multiplying,

$\Rightarrow -6 - 2a = 0 \\[0.5em] \Rightarrow 2a = -6 \\[0.5em] a = -3.$

Hence, the value of a is -3.