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The problem asks to simplify and match the expression \( 4x^2 - 3x^2 + 5x - 24 \) to one of the factored forms provided in the multiple choices. 

First, simplify the given expression:
\[
4x^2 - 3x^2 + 5x - 24 = x^2 + 5x - 24
\]
Now, we will factor this quadratic expression.

We need two numbers that multiply to \(-24\) and add up to \(5\). These numbers are \(8\) and \(-3\), so we can factor the quadratic as:
\[
x^2 + 5x - 24 = (x + 8)(x - 3)
\]

Thus, the correct answer is:
\[
\boxed{(x + 8)(x - 3)}
\]

Would you like further details or explanations? Here are some related questions to think about:
1. How do you factor a quadratic equation?
2. Why do we look for factors that multiply to a constant and add to the middle term?
3. How can you verify that your factorization is correct?
4. What methods can be used to solve quadratics other than factoring?
5. How would this problem change if the leading coefficient wasn't 1?

**Tip:** Always check your factorization by expanding to ensure you get the original expression!

Which of the following simplifies to the same expression as 4x^2 - 3x^2 + 5x - 24?

Learn how to factor the quadratic expression x^2 + 5x - 24 by finding numbers that multiply to -24 and add up to 5. A step-by-step solution is provided, with the correct answer being (x + 8)(x - 3).

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