Help with a polynomials problem!?

1.   P(x)=x^3 + 9x^2 + 24x + 20

By the Rational Roots Theorem, -2 is one root...so we have

-2     1    9      24      20

             -2     -14    -20

----------------------------

        1    7      10      0

The remaining polynomial  is x^2 + 7x + 10    which factors as (x + 2) (x + 5)

So the factorization of this is    P(x)  =  (x +2)(x + 2) (x +5)  = (x + 2)^2 (x + 5)

2.  We have

                            x^2   + 7x   + 10

             --------------------------------------------

x + 2    [  x^3  + 9x^2  + 24x  + 20 ]  

                x^3  + 2x^2

             -------------------------------------------

                           7x^2  + 24x

                            7x^2 + 14x

             --------------------------------------------

                                        10x  + 20

                                         10x + 20

             ------------------------------------------

                                                     0  remainder

So, now notice, tyler, the quotient polynomial,  x^2 + 7x + 10,   factors as before  in the first part

So the three factors  are (x + 2)(x + 2)(x + 5)  =  (x + 2) ^2 (x + 5)  .....as before....

That was a lot of effort Chris,  looks really good :)

Thanks, Melody.....