Question

3x³ − x² − 3x + 1

Answer 1

Let `f(x) = 3x^3 - x^2 - 3x + 1` be the given polynomial.

Now, putting  x = 1,we get

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

        ` = 3-1 -3 +1 = 0`

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

Now,

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

        ` = (x-1){3x^2 + 2x - 1}`

        ` = (x-1 ){3x^2 + 2x -1}`

        `= (x -1)(x+1)(3x-1)`

Hence (x -1),(x+1) and (3x - 1 )are the factors of polynomial f(x).