is divided by (x+3)

Let, f(x) = 2x⁴ + 6x³ + 2x² + x - 8

Now,

As per the question,

x - 3 = 0

x = 3

Using Remainder theorem,

We know that when f(x)is divided by (x – 3), the remainder so obtained will be f(3).

Hence,

f(3) = 2(3)⁴ + 6(3)³ + 2(3)² + 3 - 8

= 2(81) + 6(27) +18 – 5

= 18 - 11

= 7

Therefore,

The required remainder is 7.