Factoring a quadratic expression

Which correctly factored form of the function  f(x) = 36x² + 15x - 6  can be used to identify the zeros?
A.)  f(x) = (4x - 1)(3x + 2)
B.)  f(x) = (12x - 2)(3x + 3)
C.)  f(x) = 3(4x - 1)(3x + 2)
D.)  f(x) = 3(12x - 2)(3x + 3)

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Look for a common factor to factor out, first.

36x² + 15x - 6
= 3(12x² + 5x - 2)   {factored 3 out}

Factor the remaining quadratic trinomial by grouping.

12x² + 5x - 2
=  12x² + 8x - 3x - 2   {split the 5x into two terms, whose coefficients multiply to get 12(-2) and add to get 5}
=  4x(3x + 2) - 1(3x + 2)   {factored 4x out of first two terms and -1 out of last two terms}
=  (4x - 1)(3x + 2)    {factored (3x + 2) out of the two terms}

Don't forget the 3 that was factored out earlier.

C.)  f(x) = 3(4x - 1)(3x + 2)

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