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The image contains a mathematical problem in Persian related to polynomial division and finding the remainder. Let's break it down.

**Problem in Persian:**
If we have two expressions:

\[
A = 2x^3 - 4x + a - 2
\]
\[
B = x^2 + ax - 2
\]

Divided by \(2x - 4\), and the remainder is zero (meaning they are divisible), what is the value of \(a\)?

**Choices:**
1) \(a = -1\)
2) \(a = 2\)
3) \(a = 3\)
4) \(a = -4\)

### Approach:
We are asked to find the value of \(a\) such that when \(A\) and \(B\) are divided by \(2x - 4\), the remainder is zero. 

- To solve, we will apply polynomial division or use synthetic division methods to find \(a\).
- First, simplify the divisor \(2x - 4\) by factoring out 2: 
  \[
  2x - 4 = 2(x - 2)
  \]
- We perform the division of \(A\) and \(B\) by \(x - 2\) and check when the remainder is zero.

Let me perform the calculations for \(a\).It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like me to help guide you through the steps manually, or would you prefer to try again with another question?

Here are 5 related questions to expand your understanding:
1. How is synthetic division used to find remainders in polynomial division?
2. What is the role of the remainder theorem in solving polynomial divisions?
3. How do you simplify a divisor like \(2x - 4\) to \(x - 2\)?
4. What happens if the remainder is not zero when dividing polynomials?
5. How can factoring help in polynomial division problems?

**Tip:** Always simplify polynomials and divisors before attempting division to make calculations easier!

If the two expressions A = 2x^3 - 4x + a - 2 and B = x^2 + ax - 2 are divided by 2x - 4, and the remainder is zero, what is the value of a?

Learn how to solve polynomial division problems by determining the value of the unknown variable 'a' that results in a remainder of zero. This problem involves key algebraic concepts such as polynomial division and the remainder theorem, suitable for high school students.

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