Answer:
(x-2)
----------------
x^3
Explanation:
(x^2 -4) x^3 -x^2 -6x
------------ ÷ ---------------------
x^3 + 7x^2 x^2 +4x -21
Copy dot flip
(x^2 -4) x^2 +4x -21
------------ * ---------------------
x^3 + 7x^2 x^3 -x^2 -6x
Factor
(x-2)(x+2) (x+7)(x-3)
------------ * ---------------------
x^2(x+7) x(x-3)(x+2)
Cancel like terms
(x-2) 1
------------ * ---------------------
x^2 x
(x-2)
----------------
x^3