Which of the following simplifies to the same expression as 4x2−3x2+5x−24

To simplify \( 4x^2 - 3x^2 + 5x - 24 \), we can first combine the like terms:

\[
4x^2 - 3x^2 = (4 - 3)x^2 = 1x^2 = x^2
\]

So, we can rewrite the expression as:

\[
x^2 + 5x - 24
\]

Next, we will factor the quadratic expression \( x^2 + 5x - 24 \).

We need to find two numbers that multiply to \(-24\) (the constant term) and add to \(5\) (the coefficient of the linear term). The numbers \(8\) and \(-3\) satisfy this:

\[
8 + (-3) = 5 \quad \text{and} \quad 8 \times (-3) = -24
\]

So, we can factor the quadratic as:

\[
(x + 8)(x - 3)
\]

Now, we can compare this factorization with the options given:

1. \(2(x - 12)\)
2. \(4x(x - 6)\)
3. \((x + 6)(x - 4)\)
4. \((x + 8)(x - 3)\)

The correct option that simplifies to the same expression as \(4x^2 - 3x^2 + 5x - 24\) is:

\[
\boxed{(x + 8)(x - 3)}
\]