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​Algebra 1   State Test Practice

Factorization of a quadratic function

3/2/2017

 
What factorization can be used to reveal the zeros of  f(x) = -12x² - 11x + 15 ?
A.)  f(x) = -x(12x + 11) + 15
B.)  f(x) = (-4x + 3)(3x + 5)
C.)  f(x) = -(4x + 3)(3x + 5)
​D.)  f(x) = (4x + 3)(-3x + 5)

f(x) = -12x² - 11x + 15
=  -1(12x² + 11x - 15)   {factored -1 out}
=  -(12x² + 20x - 9x - 15)   {factoring by grouping......split the middle term, 11x, into 20x and -9x}
=  -[4x(3x + 5) - 3(3x + 5)]   {factored 4x out of first two terms and -3 out of last two terms}
=  -(3x + 5)(4x - 3)   {factored out the common factor, (3x + 5)}

Looking at the answer choices, the only one that matches is:

B.)  f(x) =  (-4x + 3)(3x + 5)  {distributed negative sign to (4x - 3)}

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