Question

Divide (Factor Completely) x3 +7x2 -4x -28 by (x+7)

Answer 1

                         x^2 - 4
                     ------------------------------
          x + 7   |   x^3 + 7x^2 - 4x - 28
                         x^3 + 7x^2
                     ------------------
                                        0 - 4x - 28
                                            -4x - 28
                                         -------------
                                                      0

Now we know that
x^3 + 7x^2 - 4x - 28 = (x^2 - 4)(x + 7)

x^2 - 4 can be factored since it is the difference of two squares.
x^2 - 4 = (x + 2)(x - 2)

The complete factoring is:

x^3 + 7x^2 - 4x - 28 = (x +2)(x - 2)(x + 7)