Question

An entrepreneur estimates that the total profit (profit = total revenue minus total cost) from his proposed company will be given by the function P(x) = x3 – 4x2 + 3x – 12, where P is in hundreds of dollars and x is the number of years elapsed after the company starts operations. In how many years (x) will the company break even (no profit, no loss)?

Answer 1

So I would factor it first like so:
P(x) = x^3 - 4x^2 +3x - 12
=x^2(x-4)+3(x-4)
=(x^2+3)(x-4)

Then set the factored form equal to 0 because you want the company to break even so:
P(x)=0
0=(x^2+3)(x-4)
0=x-4
4=x

x^2 +3 =0 has no real solution

So x equals four so the company will break even in 4 years