Factor the trinomial f(x) = 2x² + 5x – 12 ?

Question

Factor the trinomial f(x) = 2x² + 5x – 12 ?

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Maria 2 weeks 2021-11-23T19:15:45+00:00 1 Answer 0 views 0

Answers ( )

  1. Charlotte
    0
    2021-11-23T19:17:18+00:00

    Answer:

    (x + 4)(2x – 3)

    Step-by-step explanation:

    Given

    f(x) = 2x² + 5x – 12

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

    product = 2 × -12 = – 24 and sum = + 5

    The factors are + 8 and – 3

    Use these factors to split the x- term

    2x² + 8x – 3x – 12 ( factor the first/second and third/fourth terms )

    2x(x + 4) – 3(x + 4) ← factor out (x + 4) from each term

    (x + 4)(2x – 3)

    Thus

    f(x) = 2x² + 5x – 12 = (x + 4)(2x – 3) ← in factored form

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