Question

x³ − 2x² − x + 2

Answer 1

Let `f(x) = x^3 - 2x^2 - x + 2` be the given polynomial.

Now, putting  x =1,we get

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

               ` = 1-2 - 1+2 = 3 -3`

               ` = 0`

Therefore, (x+1)is a factor of polynomial f(x).

Now,

`f(x) = x^2 (x-1) -x(x -1) -2(x -1)`

` = (x -1){x^2 - x - 2}`

` = (x -1){x^2 - 2x + x -2}`

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

Hence  (x -1),(x+1) and (x -2)are the factors of polynomial f(x).