Question

factorise x^3-2x^2-x+2

Answer 1

${x}^{2} \times (x - 2) - ( x - 2) \\ (x - 2) \times ( {x}^{2} - 1) \\ (x - 2) \times (x - 1) \times (x + 1)$
This is ur answer

Answer 2

Let take f(x) = x3 - 2x2 - x + 2
The constant term in f(x) is are ±1 and  ±2
Putting x = 1 in f(x), we have
f(1) = (1)3 - 2(1)2 -1 + 2
= 1 - 2 - 1 + 2 = 0
According to remainder theorem f(1) = 0 so that  (x - 1) is a factor of x3 - 2x2 - x + 2
Putting x = - 1 in f(x), we have
f(-1) = (-1)3 - 2(-1)2 –(-1) + 2
= -1 - 2 + 1 + 2 = 0
According to remainder theorem f(-1) = 0 so that  (x + 1) is a factor of x3 - 2x2 - x + 2

Putting x =  2 in f(x), we have
f(2) = (2)3 - 2(2)2 –(2) + 2
= 8 -82  - 2 + 2 = 0
According to remainder theorem f(2) = 0 so that  (x – 2 ) is a factor of x3 - 2x2 - x + 2

Here maximum power of x is 3 so that its can have maximum 3 factors