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11 December, 01:12

Factoring Quadratic trinomials: 4x^2 - 13x + 3

A.) (4x + 1) (x + 3)

B.) (4x - 1) (x + 3)

C.) (4x + 1) (x - 3)

D.) (4x - 1) (x - 3)

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Answers (1)
  1. 11 December, 02:55
    0
    D

    Step-by-step explanation:

    Given

    4x² - 13x + 3

    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 = 4 * 3 = 12 and sum = - 13

    The factors are - 12 and - 1

    Use these factors to split the x - term

    4x² - 12x - x + 3 (factor the first/second and third/fourth terms)

    = 4x (x - 3) - 1 (x - 3) ← factor out (x - 3) from each term

    = (x - 3) (4x - 1)

    Thus

    4x² - 13x + 3 = (4x - 1) (x - 3) → D
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