Which of the following simplifies to the same expression as 4x2−3x2+5x−24?(1 point)

To determine which expression simplifies to the same expression as \(4x^2 - 3x^2 + 5x - 24\), we first simplify \(4x^2 - 3x^2 + 5x - 24\).

1. Combine the like terms:
\[
4x^2 - 3x^2 = (4 - 3)x^2 = 1x^2 = x^2
\]
So, the expression simplifies to:
\[
x^2 + 5x - 24
\]

Next, we can factor the expression \(x^2 + 5x - 24\):

To factor \(x^2 + 5x - 24\), we need two numbers that multiply to \(-24\) (constant term) and add to \(5\) (coefficient of \(x\)). These two numbers are \(8\) and \(-3\) because:

\[
8 \times (-3) = -24
\]
\[
8 + (-3) = 5
\]

Thus, we can factor the expression as:
\[
(x + 8)(x - 3)
\]

Now, we compare this with the provided options:

1. **\(4x(x - 6)\)** - Does not match because the degrees don't correspond.
2. **\(2(x - 12)\)** - Does not match as it simplifies to a linear term.
3. **\((x + 8)(x - 3)\)** - This matches our factored form.
4. **\((x + 6)(x - 4)\)** - Does not match because the numbers do not fit our earlier factorization.

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