To determine which expression can be compared to \( 3x^2 + 15x - 42x^2 - 4 \) and is equivalent, we first need to simplify the given polynomial.
Starting with the expression:
\[ 3x^2 + 15x - 42x^2 - 4 \]
We can combine like terms:
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Combine the \( x^2 \) terms: \[ 3x^2 - 42x^2 = -39x^2 \]
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The \( x \) term remains \( 15x \).
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The constant term remains \( -4 \).
Putting it all together, we find:
\[ -39x^2 + 15x - 4 \]
Now, let's evaluate the options provided to see which one is equivalent to this expression.
Option 1: \( 3(x+7) \)
Expanding \( 3(x + 7) \): \[ 3x + 21 \] This does not match \( -39x^2 + 15x - 4 \).
Option 2: \( 3(5x - 12) - 4 \)
Expanding this gives: \[ 3(5x - 12) - 4 = 15x - 36 - 4 = 15x - 40 \] This does not match \( -39x^2 + 15x - 4 \).
Option 3: \( (3x + 21)(x - 2) \)
Expanding this gives: \[ 3x^2 - 6x + 21x - 42 = 3x^2 + 15x - 42 \] This does not match our expression.
Option 4: \( \frac{3(x + 7)}{x + 2} \)
This form does not have the appropriate degree to match \( -39x^2 + 15x - 4 \).
Since none of these simplifications and comparisons have yielded an equivalent form to \( -39x^2 + 15x - 4 \), please check if I have correctly interpreted the original polynomial and if the provided options are indeed exhaustive lists. If you need further evaluation or a different approach, let me know!