To determine which expressions produce the trinomial \( 4x^2 - 20x - 24 \) when simplified, we can simplify each expression and check if it matches the trinomial.
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Expression: \( 4(x^2 - 5x - 6) \)
\[ = 4(x^2 - 5x - 6) = 4x^2 - 20x - 24 \]
This expression simplifies to \( 4x^2 - 20x - 24 \), so it is correct.
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Expression: \( -4(x^2 + 5x + 6) \)
\[ = -4(x^2 + 5x + 6) = -4x^2 - 20x - 24 \]
This does not match \( 4x^2 - 20x - 24 \).
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Expression: \( 4(x^2 - 20x - 24) \)
\[ = 4(x^2 - 20x - 24) = 4x^2 - 80x - 96 \]
This does not match \( 4x^2 - 20x - 24 \).
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Expression: \( -4(x^2 + 5 + 6) \)
\[ = -4(x^2 + 5 + 6) = -4x^2 - 20 - 24 \]
This does not match \( 4x^2 - 20x - 24 \).
After checking all expressions, the two that produce the trinomial \( 4x^2 - 20x - 24 \) when simplified is:
- \( 4(x^2 - 5x - 6) \)
- None of the others match.
Final answer: Only the first expression \( 4(x^2 - 5x - 6) \) is correct.