The problem asks us to find the remainder when the polynomial $f(x) = 2x^3 - 13x^2 + 14x + 24$ is divided by $(x-3)$.

1. Problem Description

The problem asks us to find the remainder when the polynomial $f(x) = 2x^3 - 13x^2 + 14x + 24$ is divided by $(x-3)$.

2. Solution Steps

To find the remainder when $f(x)$ is divided by $(x-3)$, we can use the Remainder Theorem. The Remainder Theorem states that if a polynomial $f(x)$ is divided by $(x-c)$, then the remainder is $f(c)$. In this case, we want to divide by $(x-3)$, so $c = 3$. We need to find $f(3)$.

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

$f(3) = 2(27) - 13(9) + 14(3) + 24$

$f(3) = 54 - 117 + 42 + 24$

$f(3) = 54 + 42 + 24 - 117$

$f(3) = 120 - 117$

$f(3) = 3$

3. Final Answer

The remainder when $f(x)$ is divided by $(x-3)$ is 3.