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Algebra....HELP!!

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Explain how to factor the following trinomials forms: x2 + bx + c and ax2 + bx + c. Is there more than one way to factor this? Show your answer using both words and mathematical notation.

  • Algebra....HELP!! -

    Factor x^2 + 5x + 6

    C = 6 = 1*6 = 2*3.
    Select the pair of factors whose sum equals B which is 5.
    We select 2 and 3, because their sum = 5.

    Solution: (x+2)(x+3).
    The solution can be checked by performing the multiplication and
    combining like-terms.

    Factor 2x^2 + 11x + 12.
    This and the previous example can be done by trial and error, but the process can be tedious and very frustrating.

    We'll use the AC Method:
    A*C = 2 * 12 = 24 = 3*8 = 4*3.
    We select the pair of factors whose sum = B(11). Therfore, we select 3 and 8.

    2x^2 + (3x+8x) + 12
    Arrange the 4 terms into two factorable binomials:
    (2x^2+3x) + (8x+12)
    x(2x+3) + 4(2x+3)
    (2x+3)(x+4).

    I hope this helps.

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