Let f(x) be a polynomial function. If f(x) is divided by x-1, x+1 & x+2, then remainders are 5,3 and 2 respectively. When f(x) is divided by `x^3 +2 x^2 - x - 2`, then remainder is : (A) x - 4 (b) x + 4 (c) x-2 (d) x + 2

Explanation

First, we will find factors of `x^3+2x^2-x-2`.

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

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

Let remainder is `ax^2+bx+c` and quotient is `q(x)`.

Then, with the given details, we can write,

`f(x) = q(x)(x+1)(x-1)(x+2)+ax^2+bx+c`

Now,
As remainder after dividing `(x-1)` is `5`, we can write

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