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20 November, 23:37

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.

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Answers (1)
  1. 21 November, 02:13
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    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
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