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The problem in the image you uploaded is asking to find a polynomial based on the given information about its remainders when divided by two different quadratic polynomials.

Here’s the translation and summary of the problem:

**Problem:**
A cubic polynomial, \( f(x) \), when divided by \( x^2 - 3x + 10 \) leaves a remainder of \( 3x + 2 \), and when divided by \( x^2 - 4x + 3 \) leaves a remainder of \( 28x + 17 \). Find the polynomial.

### Solution Process:

1. **Let the cubic polynomial be:**  
   \[
   f(x) = (x^2 - 3x + 10) q_1(x) + (3x + 2)
   \]
   and
   \[
   f(x) = (x^2 - 4x + 3) q_2(x) + (28x + 17)
   \]
   where \( q_1(x) \) and \( q_2(x) \) are quotient polynomials, and the remainders are \( 3x + 2 \) and \( 28x + 17 \), respectively.

2. **Set up a system of equations:**
   To find \( f(x) \), you need to consider the structure of both equations. Use the fact that the degree of \( f(x) \) is 3 and substitute specific values of \( x \) to find \( f(x) \).

Would you like to continue with solving the system or need more clarification? 

Here are 5 related questions to expand on this topic:

1. How can we find the general form of a polynomial of degree 3?
2. What is the remainder theorem, and how does it apply to polynomial division?
3. How can we solve a system of equations involving polynomials?
4. What are the different methods for dividing polynomials?
5. Can you derive \( f(x) \) if only one remainder is given?

**Tip:** When working with polynomials, synthetic division is a powerful tool to simplify division problems.

Suatu suku banyak berderajat tiga jika dibagi (x^2 - 3x + 10) bersisa 3x + 2, dan jika dibagi (x^2 - 4x + 3) bersisa 28x + 17. Maka suku banyak tersebut adalah ... .

Solve a cubic polynomial problem where f(x) leaves remainders when divided by two quadratic polynomials, x^2 - 3x + 10 and x^2 - 4x + 3. This example involves polynomial division and the remainder theorem, suitable for students in Grades 10-12.

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