is divided by (x-2)

Let, f(x) = 3x⁴ – 6x² - 8x + 2

Now,

As per the question,

x – 2 = 0

x = 2

Using Remainder theorem,

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

Hence,

f(2) = 3(2)⁴ – 6(2)² - 8(2) + 2

= 3(16) – 6(4) -16 + 2

= 48 -24 – 14

= 10

Therefore,

The required remainder is 10.