If (x+1) is one factor of x^3 + 2x^2 + kx -6 find the other factors

As (x + 1) is a factor, it follows that












Now we can use long division to find what is left of f(x) after it is divided by (x + 1). (Apologies, this is the best way I can represent long division on at this current time - I hope it's clear)

           x^2 +   x   -   6
x + 1 ( x^3 + 2x^2 - 5x - 6
           x^3 +   x^2
                       x^2 - 5x
                       x^2 + x
                               -6x - 6
                               -6x - 6
                                        0

So the remainder when f(x) is divided by (x + 1) is


Factorising this we get


So the three factors of f(x) are (x + 1), (x + 3) and (x - 2).