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Let's analyze the mathematical problems presented in the image.

### Câu 4:
Given the polynomial \( A(x) = 2x^3 - 3ax + 5 \) (where \( a \) is a constant), find \( a \) such that \( P(2) = 3 \).

First, we interpret this question as requiring us to substitute \( x = 2 \) into the polynomial \( A(x) \) and set it equal to 3, then solve for \( a \).

\[
A(2) = 2(2^3) - 3a(2) + 5 = 3
\]
\[
A(2) = 2(8) - 6a + 5 = 3
\]
\[
16 - 6a + 5 = 3
\]
\[
21 - 6a = 3
\]
\[
-6a = 3 - 21
\]
\[
-6a = -18
\]
\[
a = 3
\]

So, the value of \( a \) is **3**.

### Câu 5:
Given:
- \( F(x) = x^{2n} - x^{2n-1} + \dots + x^2 - x + 1 \)
- \( G(x) = -x^{2n+1} + x^{2n} - x^{2n-1} + \dots + x^2 - x + 1 \)

We are asked to calculate the value of \( F(x) - G(x) \) at \( x = 2 \).

Let's first subtract \( G(x) \) from \( F(x) \):
\[
F(x) - G(x) = \left( x^{2n} - x^{2n-1} + \dots + x^2 - x + 1 \right) - \left( -x^{2n+1} + x^{2n} - x^{2n-1} + \dots + x^2 - x + 1 \right)
\]
This simplifies to:
\[
F(x) - G(x) = x^{2n+1}
\]

Now, substitute \( x = 2 \):
\[
F(2) - G(2) = 2^{2n+1}
\]

Thus, the value of \( F(2) - G(2) \) is \( 2^{2n+1} \).

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Let me know if you'd like further details or explanations.

### Related Questions:
1. Can you explain why the highest degree term dominates the subtraction in Câu 5?
2. What happens if \( x = -2 \) in the expression for \( F(x) - G(x) \)?
3. How would you derive the general form of \( F(x) - G(x) \) for arbitrary \( x \)?
4. What is the significance of solving for \( a \) in Câu 4 if \( A(x) \) had additional terms?
5. How does changing the degree of the polynomial \( F(x) \) affect the behavior of the function as \( n \) increases?

### Tip:
When dealing with polynomials, always look for patterns or simplifications when subtracting similar functions!

Solve the following mathematical problems:
1. Find the value of 'a' such that A(2) = 3 for the polynomial A(x) = 2x^3 - 3ax + 5.
2. Calculate the value of F(x) - G(x) at x = 2, where F(x) = x^2n - x^(2n-1) + ... + x^2 - x + 1 and G(x) = -x^(2n+1) + x^2n - x^(2n-1) + ... + x^2 - x + 1.

Learn how to solve a polynomial problem by finding the constant 'a' in A(x) = 2x^3 - 3ax + 5, and calculate the value of F(x) - G(x) at x = 2 for higher-degree polynomials. Suitable for high school students, Grades 10-12.

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