is divided by (x-6)

Let, f(x) = x³ – 7x² + 6x + 4

Now,

As per the question,

x – 6 = 0

x = 6

Using Remainder theorem,

We know that when f(x) is divided by (x – 6), the remainder so obtained will be f(6).

Hence,

f(6) = (6)³ – 7(6)² + 6(6) + 4

= (216) – 7(36) + 36 + 4

= 256 -252

= 4

Therefore,

The required remainder is 4.