Question

x³ − 10x² − 53x − 42

Answer 1

Let  `f(x) = x^3 - 10x^2 - 53x -42` be the given polynomial.

Now, putting  x = -1 we get

`f(-1) = (-1)^3 - 10(-1)^2 - 53(-1) - 42`

             ` = -1-10 + 53 - 42`

             ` = -53 + 53 = 0`

 

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

Now,

`f(x) = x^2 (x+1) -11x(x+1) - 42(x+1)`

` = (x+1){x^2 -11x - 42}`

` = (x + 1){x^2 - 14x + 3x - 42}`

` = (x +1)(x+3)(x - 14)`

Hence  (x+1),(x + 3) and (x - 14)are the factors of polynomial f(x).