The problem states that a polynomial $f(x) = 2x^3 - 13x^2 + 14x + 24$ is divided by something, but the divisor is not fully specified. It asks to find the remainder. However, without knowing the divisor, it is impossible to uniquely determine the remainder. I will assume that the question asks for the remainder when $f(x)$ is divided by $(x-6)$.

1. Problem Description

The problem states that a polynomial $f(x) = 2x^3 - 13x^2 + 14x + 24$ is divided by something, but the divisor is not fully specified. It asks to find the remainder. However, without knowing the divisor, it is impossible to uniquely determine the remainder. I will assume that the question asks for the remainder when $f(x)$ is divided by $(x-6)$.

2. Solution Steps

Since we want to find the remainder when $f(x) = 2x^3 - 13x^2 + 14x + 24$ is divided by $(x-6)$, we can use the Remainder Theorem. The Remainder Theorem states that if a polynomial $f(x)$ is divided by $(x-c)$, the remainder is $f(c)$. In this case, $c = 6$.

We evaluate $f(6)$:

$f(6) = 2(6)^3 - 13(6)^2 + 14(6) + 24$

$f(6) = 2(216) - 13(36) + 84 + 24$

$f(6) = 432 - 468 + 84 + 24$

$f(6) = 432 - 468 + 108$

$f(6) = 540 - 468$

$f(6) = 72$

3. Final Answer

The remainder when $f(x) = 2x^3 - 13x^2 + 14x + 24$ is divided by $(x-6)$ is $72$.