Let, f(x) = 81x⁴ + 54x³ – 9x² - 3x + 2

Now,

As per the question,

3x + 2 = 0

3x = -2

x =

Using Remainder theorem,

We know that when f(x)is divided by (2x – 1), the remainder so obtained will be .

Hence,

= 16 – 16 + 4 - 4

= 0

Therefore,

The required remainder is 0.