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To solve the problem, we are asked to find the remainder when dividing the polynomial \( x^3 - 3x^2 + 2 \) by \( x - 1 \).

This can be done using **synthetic division** or by directly applying the **remainder theorem**, which states that the remainder of dividing a polynomial \( f(x) \) by \( x - a \) is equal to \( f(a) \).

### Steps:
1. The divisor is \( x - 1 \), so we substitute \( x = 1 \) into the polynomial \( f(x) = x^3 - 3x^2 + 2 \).
   
   \[
   f(1) = (1)^3 - 3(1)^2 + 2 = 1 - 3 + 2 = 0
   \]

2. The remainder is \( 0 \).

Thus, the remainder when dividing \( x^3 - 3x^2 + 2 \) by \( x - 1 \) is **0**.

The correct answer is **0** (last option in the list).

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Do you need more details or have any questions? Here are 5 related questions to explore further:

1. How does synthetic division work for polynomials?
2. What is the remainder theorem and when should it be applied?
3. How do you factor cubic polynomials?
4. Can you always use the remainder theorem to find remainders in division?
5. What happens if the divisor is more complex, like \( x^2 - x + 1 \)?

**Tip:** When dividing a polynomial by \( x - a \), always try the remainder theorem first as it gives quick results!

باقي قسمة (x^3 - 3x^2 + 2) على (x - 1) يساوي؟

Learn how to find the remainder when dividing the polynomial x^3 - 3x^2 + 2 by x - 1. This problem covers key algebraic concepts, including the remainder theorem. Suitable for high school students (Grades 9-12).

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