Using remainder theorem, find the value of a if the division of x³ + 5x² - ax + 6 by (x - 1) leaves the remainder 2a.

By remainder theorem, on dividing f(x) by (x - a) , remainder = f(a)

∴ On dividing, f(x) = x³ + 5x² - ax + 6 by (x - 1)

Remainder = f(1)

Given, remainder = 2a

$\therefore (1)^3 + 5(1)^2 - a(1) + 6 = 2a \\[0.5em] \Rightarrow 1 + 5 - a + 6 = 2a \\[0.5em] \Rightarrow 12 - a = 2a \\[0.5em] \Rightarrow 3a = 12 \\[0.5em] a = 4 \\[0.5em]$

Hence, the value of a is 4.