Question

x³ − 3x² − 9x − 5

Answer 1

Let  `f(x) = x^3 - 3x^2 - 9x -5 ` be the given polynomial.

Now, putting  x = 1,we get

`f(-1) = (-1)^3 -3(-1)^ -9(-1) - 5`

             `=-1 -3 +9 -5 = -9 +9 = 0`

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

Now,

`f(x) = x^2 (x+1) -4x(x+1) -5(x +1)`

` = (x+1){x^2 -4x -5}`

` =(x+1){x^2 - 5x + x -5}`

` = (x+1)(x+1)( x-5)`

Hence  (x+1) , (x+1) and (x - 5) are the factors of polynomial f(x) .