the profit is a polynomial function :
p(x) = x^4 − x^3 − 24
the average profit per unit of product sold is :
ap(x) = (x^4 − x^3 − 24)/(x+2)
now,
(-2) is an "obvious" zero of p(x)
therefore : p(x) is dividable by (x+2)
and
the long division of p(x) by (x+2) gives :
Answer:
ap(x) = x^3 - 3x^2 + 6x - 12
