Expert: Richard J. Raridon - 7/26/2009

Question
Would you please show me the steps on how to factor: x^3-4x^2-11x-6. From another website I found that this factors to:(x-6)(x+1)^2 This site did not show how to do this, step by step. When I tried to do this, I factored this last constant term "6": 1,2,3,6. I plugged these factors, one at a time, both negative and positive into the x variable of this polynomial. I found that -1 and 6 were viable roots. Therefore I figured that these factors would be : (x+1)(x-6). These factors when multiplied do not produce the original polynomial. Also, the first term has an exponent of 3 which indicates that there should be 3 factors, so I know that I am wrong and the other website is correct. But why? Please help me to understand this. My method must be missing something?
               Thank very much,
                              Noel

Answer
If you multiply (x+1) and (x-6) you get x^2-5x-6.  
If you then divide that into x^3-4x^2-11x-6 the answer would be (x+1).  Actually, you could have seen that the final answer would have to be x=1 or x=-1 since you already have the 6.  And since it's already -6 then you would have to multiply by 1 to keep it -6, leading you to (x+1).  What threw you was having two identical factors.