Answer:

(x - 1)(x^ - 2x + 3).

Step-by-step explanation:

f(1) = 1^3 - 3(1)^2 + 5(1) - 3

= 1 - 3 + 5 - 3

= 6 - 6 = 0.

So, by the Factor Theorem,  (x - 1) is one factor.

Dividing f(x) by x-3 we get

x - 1) x^3 - 3x^2 + 5x - 3 ( x^2 - 2x + 3 <--- Quotient

        x^3 - x^2

                -2x^2 + 5x

                -2x^2 + 2x

                               3x - 3

                               3x - 3

x^2 - 2x + 3 is prime so the factors are:

(x - 1)(x^ - 2x + 3)