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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 -

    1. Factor: x^2 - 2x - 3.

    C = -3 = 1*(-3) = -1*3.
    Select the pair whose algebraic sum = -2(1,and-3).
    (x+1)(x-3).
    The above method works best when the coefficient of x^2 is 1.

    2. Factor: 2x^2 + x - 6.
    The AC method should be used when the
    coefficient of x^2 is not 1:

    A*C=2*(-6) = -12 = -1*12 = -2*6 = -3*4.
    Use the pair of factors whose algebraic
    sum = B(1):
    2x^2 + (-3x+4x) - 6.
    Arrange the 4 terms to form 2
    factorable binomials:
    (2x^2+4x) + (-3x-6)
    Factor each binomial:
    2x(x+2) + -3(x+2)
    (x+2)(2x-3).

    These 2 methods take all of the guess work out of factoring.

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