Question

Using factor theorem, factorize each of the following polynomial: 

x³ - 2x² - x + 2

Answer 1

Let, f (x) = x³ - 2x² - x + 2

The factors of the constant term +2 are \(\pm\) 1, \(\pm\) 2

Putting x = 1, we have

f (1) = (1)³ – 2 (1)² – (1) + 2

= 1 – 2 – 1 + 2

= 0

So, 

(x - 1) is a factor of f (x)

Let us now divide

f (x) = x³ - 2x² - x + 2 by (x - 1) to get the other factors of f (x)

Using long division method, we get

x³ - 2x² - x + 2 = (x - 1) (x² - x - 2)

x² - x - 2 = x² - 2x + x - 2

= x (x - 2) + 1 (x - 2)

= (x + 1) (x - 2)

Hence, 

x³ - 2x² - x + 2 = (x - 1) (x + 1) (x - 2)