how to factorize: x3 - 3x2 + 4

how to factorize:
x³ - 3x² + 4

Let p (x) = x^{3} - 3 x^{2} + 4 Put x = 2, we get p (2) = 2^{3} - 3 {(2)}^{2} + 4 = 8 - 12 + 4 = 12 - 12 = 0 So, (x - 2) is a factor of p (x) Now, to obtain the remaining factors, we will divide p (x) by (x - 2) using long division method .

So, p (x) = (x - 2) (x^{2} - x - 2) = (x - 2) [x^{2} - 2 x + x - 2] = (x - 2) [x (x - 2) + 1 (x - 2)] = (x - 2) (x + 1) (x - 2)