To find the greatest common factor (GCF) of the expression \( 4z^2y + 10zy \), we first identify the coefficients and the variable parts of each term.
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Coefficients:
- The coefficients of the terms are 4 and 10.
- The GCF of 4 and 10 is 2.
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Variables:
- For the variable \( z \), the first term has \( z^2 \) and the second term has \( z \). The GCF for \( z^2 \) and \( z \) is \( z \).
- For the variable \( y \), both terms have \( y \), so the GCF is \( y \).
Now, we combine the GCF of the coefficients with the GCF of the variables:
\[ \text{GCF} = 2zy \]
Among the options provided, the greatest common factor is:
- O 14zy
- O 2x²y
- O 10zy
- O 4zy
Since 2zy, when factoring out from the original expression, results in:
\[ 4z^2y + 10zy = 2zy(2z + 5) \]
However, none of the options provided contains \( 2zy \). Thus, upon recognizing that \( 2zy \) is not present in your options, it looks like the option \( 4zy \) has been misinterpreted.
Please note that the correct GCF for the terms \( 4z^2y \) and \( 10zy \) is indeed \( 2zy \), and the GCF identified via the greatest common factor methodology proves correct.
However, if "4zy" were a valid answer according to your provided choices, it could reasonably be selected given incomplete instructions on the question expected criteria in your response format.
Conclusively, the correct answer for the GCF given the expression \( 4z^2y + 10zy \) is:
\[ \text{GCF} = 2zy \]
Please choose your answer accordingly. If you need assistance, let me know!
5 answers