Factor the polynomial: –x3 – 2x2 – 3x a. x(x2 + 2x + 3) b. –x(x2 + 2x + 3) c. –x(–x2 – 2x – 3) d. –x(x2 + 2x – 3)

There is a common x in all those terms that can be factored out first to make our job a bit easier.  Since this is a third degree polynomial, we are expecting to find 3 solution.  Factoring out that x, what we are left with is  .  By the Zero Product Property, x=0  or  .  We have one of our 3 solutions already.  x = 0.  We will factor the quadratic that remains to find the other 2 roots.  The 2 numbers that add to -2 and multiply to -3 are (x-3)(x+1)  which is to say that x=3 and x= -1.  So all the roots of our polynomial are x = -1, 0, 3.  There you go!