Final answer:
The question about multiplying the function f(x) with the binomial (x - 2) requires a polynomial multiplication process, resulting in a new polynomial rather than a single numeric answer. The provided options A, B, C, and D are single numbers that do not represent the result of this algebraic operation. Additional context or a complete answer is needed to determine the correct choice.
Step-by-step explanation:
The result of multiplying the function f(x) = 4x^3 - 14x^2 + 9x + 2 with the binomial (x - 2) is not specified by one of the given options (A: 4, B: 6, C: -2, D: -4), because those options seem to pertain to a single numeric result. Multiplying a polynomial by a binomial is a standard operation in algebra that will produce another polynomial. The procedure is to distribute each term of the binomial across the polynomial and combine like terms.
Let's multiply f(x) by the binomial (x - 2):
- First, multiply 4x^3 by x and by -2.
- Next, multiply -14x^2 by x and by -2.
- Then, multiply 9x by x and by -2.
- Finally, multiply 2 by x and by -2 and combine all the like terms.
However, without additional context or a complete answer, we cannot determine which choice is correct. The related details provided in the question seem to refer to quadratic equations and their solutions using the quadratic formula, which is not directly related to the original question about multiplying a polynomial by a binomial.