3) Which of the equivalent expressions for P (x) reveals the profit when the price is

zero without changing the form of the expression?

a) P (x) = - 3x2 + 432x - 1680

b) P (x) = - 3 (x - 4) (x - 140)

c) P (x) = - 3 (x - 72) 2 + 13872

4) Find the profit when the price is zero.

Question:

Which of the equivalent expressions for P (x) reveals the profit when the price is

zero without changing the form of the expression? P (x) = - 3x² + 432x - 1680

a) P (x) = - 3 (x - 4) (x - 140)

b) P (x) = - 3 (x - 72) ² + 13872

Find the profit when the price is zero

Answer:

- P (x) = - 3 (x - 140) (x - 4).

- P (0) = - 1680

Step-by-step explanation:

Given

P (x) = - 3x² + 432x - 1680

Required

- Find equivalent of P (x)

- Find P (x) when x = 0

To find the equivalent of P (x), we simply factorize P (x) = - 3x² + 432x - 1680.

This is done as follows

P (x) = - 3x² + 432x - 1680

P (x) = - 3x² + 12x + 420x - 1680

P (x) = - 3x (x - 4) + 420 (x - 4)

P (x) = (-3x + 420) (x - 4)

Further expand - 3x + 420

P (x) = - 3 (x - 140) (x - 4).

Hence, the equivalent of

P (x) = - 3x² + 432x - 1680

without changing its form is

P (x) = - 3 (x - 140) (x - 4).

When price is 0, then x = 0.

Substitute 0 for P (x) in P (x) = - 3 (x - 140) (x - 4).

P (0) = - 3 (0 - 140) (0 - 4).

P (0) = - 3 (-140) (-4)

P (0) = - 1680

Hence, the profit when price is 0 is - 1680