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)

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)}

**- Algebra House**