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We are given a cubic polynomial \( P(x) = x^3 - rx^2 + x - 2024 \) with roots \( r \), \( s \), and \( t \), and we are tasked with finding \( P(2024) \).

### Step 1: Using Vieta’s Formulas
From Vieta’s relations, for the cubic polynomial \( P(x) = x^3 - rx^2 + x - 2024 \), the coefficients of the polynomial relate to the roots \( r \), \( s \), and \( t \) as follows:
- \( r + s + t = r \) (sum of the roots),
- \( rs + rt + st = 1 \) (sum of the products of the roots taken two at a time),
- \( rst = 2024 \) (the product of the roots).

### Step 2: Evaluating \( P(2024) \)
Since \( r \), \( s \), and \( t \) are the roots of the polynomial, \( P(x) \) can also be written as:
\[
P(x) = (x - r)(x - s)(x - t)
\]
Substituting \( x = 2024 \) into this expression, we get:
\[
P(2024) = (2024 - r)(2024 - s)(2024 - t)
\]
Thus, \( P(2024) = (2024 - r)(2024 - s)(2024 - t) \).

Since \( r \), \( s \), and \( t \) are the roots, \( rst = 2024 \). The value \( P(2024) \) corresponds to substituting \( x = 2024 \) into the expression, giving us the result for the polynomial evaluated at 2024.

### Answer: 
Based on this analysis, the correct answer is \( P(2024) = 2024 \), corresponding to option **d**.

Let me know if you need further clarification or details. 

### Related Questions:
1. How does Vieta’s theorem help in finding the sum and product of roots in polynomials?
2. Can we find other values of \( P(x) \) given different values of \( x \)?
3. How does the structure of a cubic polynomial affect its graph?
4. What is the significance of evaluating a polynomial at its roots?
5. How would the solution change if the constant term in the polynomial was different?

#### Tip: 
Always check for symmetry in the polynomial when the problem involves substituting large values of \( x \), as this can simplify the computations significantly.

Misalkan P(x) = x^3 − rx^2 + x − 2024 adalah sebuah polinomial dengan akar-akar r, s, dan t. Berapakah nilai dari P(2024)?

Learn how to evaluate the cubic polynomial P(x) = x^3 − rx^2 + x − 2024 at x = 2024 using Vieta's relations. This solution covers key polynomial concepts and is suitable for high school students.

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