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Let's simplify the expression \(4x^2 - 3x^2 + 5x - 24\).
1. Combine the like terms:
\[
4x^2 - 3x^2 = x^2
\]
So the expression becomes:
\[
x^2 + 5x - 24
\]
2. Next, we need to factor this expression \(x^2 + 5x - 24\). We need two numbers that multiply to \(-24\) (the constant term) and add to \(5\) (the coefficient of the \(x\) term). The numbers \(8\) and \(-3\) satisfy these conditions:
\[
8 \times (-3) = -24 \quad \text{and} \quad 8 + (-3) = 5
\]
3. Therefore, we can factor the expression:
\[
x^2 + 5x - 24 = (x + 8)(x - 3)
\]
Now, we can match our result with the provided options. The expression that simplifies exactly to \(4x^2 - 3x^2 + 5x - 24\) is:
\((x + 8)(x - 3)\)
So, the correct answer is \((x + 8)(x - 3)\).