is divided by (x-1)

Let, f(x) = x³ – 6x² + 9x + 3

Now,

As per the question,

x – 1 = 0

x = 1

Using Remainder theorem,

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

Hence,

f(1) = (1)³ – 6(1)² + 9(1) + 3

= 1 – 6 + 9 + 3

= 13 – 6

= 7

Therefore,

The required remainder is 7