Question

The profit function for a product is given by π(x) = −x
3 + 28x
2 − 57x − 450,
where x is the number of units produced and sold. If break-even occurs when 6
units are produced and sold:
i. Find the quadratic factor of π(x).
ii. Find a number of units other than 6 that gives break-even for the product

Answer 1

Thank you for asking this question. Here is your answer:

π(x) = −x

3 + 28x

2 − 57x − 450

First of all we will divide the above equation by 10

It will give us -188180 and the remainder for this would be 0

And when you factorize this further you will get the following:

(-x2 + 88x + 180)(x-10)

-(x-90)(x+2)(x-10)

If there is any confusion please leave a comment below.