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 $2^{2n+1}$.

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!