Final answer:
To determine the factored equivalent of the quadratic expression (-24x² - 68x + 12(x+7)), we first simplify and then factor the resulting quadratic. Without the full factoring process provided, we cannot conclusively identify the correct option. However, we can exclude options with incorrect factorization.
Step-by-step explanation:
The factored equivalent form of the given quadratic expression (f(x) = (-24x² - 68x + 12(x+7)) is determined by first simplifying the expression and then factoring the resulting quadratic equation. To find the zeros of the function, we would typically set the factored form equal to zero and solve for x.
To simplify the original expression, we distribute the 12 across (x+7), resulting in -24x² - 68x + 12x + 84. Simplifying further, we get -24x² - 56x + 84. Now we need to factor this quadratic.
To factor, we look for two numbers that multiply to give a*c (where a is the coefficient of x² and c is the constant term) and add to give b (the coefficient of x). However, without the full factoring process provided in this question, we can't definitively select one of the options provided (a, b, c, or d). Yet it should be noted that option b and d contain a term (4x - 34), which can't be correct since 34 is not a factor of 84. Therefore, we are left to decide between a and c.