Final answer:
To find f(0), you can substitute x=0 into the given expressions. Both expressions 30x² - 105x - 60 and (5x-20)(6x+3) define the same function f. However, (5x-20)(6x+3) may be slightly easier to evaluate.
Step-by-step explanation:
To find f(0), we need to substitute x=0 into the expression. Let's evaluate each expression to determine which one is easier.
Evaluating 30x² - 105x - 60:
Substituting x=0 into the expression:
30(0)² - 105(0) - 60 = -60
Evaluating (5x-20)(6x+3):
Substituting x=0 into the expression:
(5(0)-20)(6(0)+3) = (-20)(3) = -60
The expressions 30x² - 105x - 60 and (5x-20)(6x+3) yield the same value when x=0. Therefore, both expressions define the same function f. However, the expression (5x-20)(6x+3) may be slightly easier to evaluate since it involves simpler arithmetic with smaller coefficients and fewer terms.