To determine which expression simplifies to \( 4x^2 - 3x^2 + 5x - 24 \), let's first simplify the given expression:
- Combine like terms for \( 4x^2 - 3x^2 \): \[ 4x^2 - 3x^2 = 1x^2 = x^2 \] So now we have: \[ x^2 + 5x - 24 \]
Next, let's factor \( x^2 + 5x - 24 \).
We are looking for two numbers that multiply to \(-24\) (the constant term) and add to \(5\) (the coefficient of \(x\)). The numbers \(8\) and \(-3\) meet these criteria, since \(8 \times -3 = -24\) and \(8 + (-3) = 5\).
Thus, we can factor the expression: \[ x^2 + 5x - 24 = (x + 8)(x - 3) \]
Now, comparing with the given options:
- \( (x + 8)(x - 3) \)
- \( 4x(x - 6) \)
- \( 2(x - 12) \)
- \( (x + 6)(x - 4) \)
The first option, \( (x + 8)(x - 3) \), is the same as \( x^2 + 5x - 24 \).
Thus, the correct response is: \[ \boxed{(x + 8)(x - 3)} \]
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