Algebra

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For what real number k does 3x^2  k factor as
3(x  2)(x + 2)?
Can someone please help with this question? I can not understand how it says to solve this in the book

  • Algebra -

    Y = 3X^2 + K
    Vertex Form:
    Y = a(X -h)^2 + k
    = 3(X -0)^2 + K

    Y = 3(X-2)(X+2),
    = 3(X^2 -4)
    = 3X^2 - 12
    h = -b / 2a = 0 / 6 = 0.
    K = Yv = 3*0^2 -12 = -12. V(0 , -12).

    Let's use a positive 2 in the 1st
    parenthesis of our factored Eq.
    Y = 3(X + 2 )(X + 2) = 3(X + 2)^2 =
    3(X^2 + 4X + 4) = 3X^2 + 12X + 12.

    h = Xv = -b / 2a = -12 / 6 = -2.
    This value of h does not agree with
    our given Eq in which h = 0.
    Therefore, -2 is the correct choice.

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