Using factor theorem, factorize each of the following polynomial:

Question

Using factor theorem, factorize each of the following polynomial: x 3 -2 x 2 - x +2

Philoid · Accepted Answer

Let, f (x) = x³-2x²-x+2

The factors of the constant term +2 are

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)

= (x - 1) (x + 1) (x – 2)