Question

x³ + 2x² − x − 2

Answer 1

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

Now, put the x = -1, we get

\[f( - 1) = \left( - 1 \right)^3 + 2 \left( - 1 \right)^2 - \left( - 1 \right) - 2\]

\[ = 0\]

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

Now, x³ + 2x² − x − 2 can be written as,

\[f(x) = x^3 + 3 x^2 - x^2 - 3x + 2x - 2\]

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

`= (x-1){x^2  + 3x + 2}`

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

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