To find the quotient when dividing \( 56r - 124t \), we need to factor the expression first.
We can factor out the greatest common factor (GCF) from the terms \( 56r \) and \( -124t \). The GCF of 56 and 124 is 28:
\[ 56r - 124t = 28(2r - 4.428t) \]
Now, we can divide by a common factor for a simplified expression, but since the question asks directly for the quotient of \( 56r - 124t \), we proceed to write down the options given:
- \( 14r - 3 \)
- \( 14r - 3t \)
- \( 11rt \)
- \( 11 \)
At this point, we can check which, if any, of these options represent a valid quotient based on manipulating \( 56r - 124t \).
If we simply divide the whole expression \( 56r - 124t \) by \( 4 \):
\[ \frac{56r}{4} - \frac{124t}{4} = 14r - 31t \]
This doesn't match any options, so let's analyze potential common factor distributions.
On revisiting these options, it’s clear that none of the options provided seem to connect directly. We can say that if evaluated as cubes or any polynomial because there are several terms and we have common t representations. Therefore, the answer is a bit vague here.
To summarize, this does not provide a valid quotient among provided responses. If there was a divisor stipulated and that was not given, we could conclude better.
Thus, the best approach is not yielding any of the options:
- None of the responses \( 14r-3 \), \( 14r-3t \), \( 11rt \), or \( 11 \) accurately reflects quotient based on dividing \(56r - 124t\).
Please check your problem statement for any additional context on division or simultaneous factors!
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