To determine which student's expression has a greatest common factor (GCF) of \(8c\), we need to factor each expression and see if \(8c\) is the GCF.
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Tanya's expression: \[ 32c + 16cd \] The coefficients \(32\) and \(16\) have a GCF of \(16\). Factoring out \(16\), we get: \[ 16(2c + cd) \] Since \(c\) is not factored out, \(8c\) is not a common factor.
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Wyatt's expression: \[ 8c - 48cd \] The coefficients \(8\) and \(48\) have a GCF of \(8\). Factoring out \(8\), we get: \[ 8(c - 6cd) \] Since \(c\) is not factored out completely (as \(c - 6cd\) cannot have \(c\) factored fully), \(8c\) is not the GCF.
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Xavier's expression: \[ 36c - 24c \] The coefficients \(36\) and \(24\) have a GCF of \(12\). Factoring out \(12\), we get: \[ 12(3c - 2c) \] Since \(c\) is part of both terms, the GCF is \(12\), not \(8c\).
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Yang's expression: \[ 8c + 40 \] The coefficients \(8\) and \(40\) have a GCF of \(8\). Factoring out \(8\), we get: \[ 8(c + 5) \] Here, \(c + 5\) cannot be factored further, so again, the GCF is indeed \(8\), but does not have \(c\) factored completely.
Since none of the expressions can maintain \(8c\) as the true GCF, we can conclude:
- None of the entries matches the condition for the GCF.
Therefore, none of the students wrote the correct expression.
1 answer