What is f(2) if dividing f(x) by (x-1) the quotient is x^2-2x+3 and the reminder is 1?

To determine the value of the polynomial f(x), when x=2,
we'll have to find out the expression of f(x).

We'll
determine the order of polynomial f(x), based on the given orders of, divisor, quotient
and reminder.

f(x)'s order = quotient's order + divisor's
order

f(x)'s order = 2 +
1

f(x)'s order = 3 order

We'll
write the reminder theorem:

f(x) = divisor*quotient +
remainder

f(x) = (x-1)*(x^2 -2x+3)+
1

We'll replace x by 3:

f(2) =
(2-1)*(2^2 -4+3)+ 1

The value of the
polynomial f(x), if x = 2, is: f(2) = 4.