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22 April, 22:14

What is the factorization of the trinomial below 3x^3-24x^2+45x

A. 3 (x-3) (x+5)

B. 3 (x^2-3) (x+5)

C. 3x (x-3) (x-5)

D. 3x (x-3) (x-5)

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Answers (1)
  1. 22 April, 23:46
    0
    1st factor is 3x:

    = 3x (x² - 8x + 15)

    2nd & 3rd factors:

    x² - 8x + 15 = 0

    x² - 4x = - 15 + ( - 4) ²

    x² - 4x = - 15 + 16

    (x - 4) ² = 1

    x - 4 = 1

    = x - 4 - 1, = x - 5

    = x - 4 + 1, = x - 3

    Answer: 3x (x - 5) (x - 3) are the factors.

    Proof:

    = 3x (x - 5) (x - 3)

    = 3x (x² - 5x - 3x + 15)

    = 3x (x² - 8x + 15)

    = 3x³ - 24x² + 45x
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