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11 June, 03:55

Factor completely, then place the answer in the proper location on the grid.

6 х^2 - 3 х - 30

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Answers (1)
  1. 11 June, 04:03
    0
    3 (x + 2) (2x - 5)

    Step-by-step explanation:

    Given

    6x² - 3x - 30 ← factor out 3 from each term

    = 3 (2x² - x - 10) ← factor the quadratic

    Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x - term

    product = 2 * - 10 = - 20 and sum = - 1

    The factors are + 4 and - 5

    Use these factors to split the x - term

    2x² + 4x - 5x - 10 (factor the first/second and third/fourth terms)

    = 2x (x + 2) - 5 (x + 2) ← factor out (x + 2) from each term

    = (x + 2) (2x - 5), thus

    2x² - x - 10 = (x + 2) (2x - 5) and

    6x² - 3x - 30

    = 3 (x + 2) (2x - 5) ← in factored form
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