To determine which expression simplifies to the same as \( 4x^2 - 3x^2 + 5x - 24 \), we first simplify the original expression.
Starting with \( 4x^2 - 3x^2 + 5x - 24 \): \[ 4x^2 - 3x^2 = x^2 \] So, we can rewrite the expression as: \[ x^2 + 5x - 24 \]
Next, we will factor \( x^2 + 5x - 24 \). We need two numbers that multiply to \(-24\) and add up to \(5\). The numbers \(8\) and \(-3\) work, so we can factor the expression as: \[ (x + 8)(x - 3) \]
Now let's check which of the provided expressions simplifies to this:
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\((x + 8)(x - 3)\) - We have already established that this is the correct factorization.
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\((x + 6)(x - 4)\): \[ = x^2 - 4x + 6x - 24 = x^2 + 2x - 24 \quad \text{(not the same)} \]
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\(4x(x - 6)\): \[ = 4x^2 - 24x \quad \text{(not the same)} \]
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\(2(x - 12)\): \[ = 2x - 24 \quad \text{(not the same)} \]
The only expression that simplifies to the same as \( 4x^2 - 3x^2 + 5x - 24 \) is: \[ \boxed{(x + 8)(x - 3)} \]
1 answer