Question
Factor out the greatest common factor from the following polynomial \( 7 y^{5}-28 x y^{6} \) Select the correct choice below and, if necessary, fill in the answer
Ask by Flynn Carroll. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The factored form of the polynomial \(7y^{5} - 28xy^{6}\) is \(7y^{5}(1 - 4xy)\).
Solution
1. Identify the greatest common factor (GCF) in both terms:
- Numerical coefficients: The numbers are \(7\) and \(-28\), and the GCF is \(7\).
- Variable factors: The first term has \(y^5\) and the second term has \(y^6\), so the GCF is \(y^5\) (the lower power).
2. Factor out \(7y^5\) from each term:
\[
7y^5 - 28xy^6 = 7y^5\left( \frac{7y^5}{7y^5} - \frac{28xy^6}{7y^5} \right)
\]
Simplify each term inside the parentheses:
- The first term: \(\frac{7y^5}{7y^5} = 1\).
- The second term: \(\frac{-28xy^6}{7y^5} = -4xy\).
3. Write the completely factored form:
\[
7y^5 - 28xy^6 = 7y^5(1 - 4xy)
\]
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Simplify this solution Mind Expander
To factor out the greatest common factor from the polynomial \( 7y^5 - 28xy^6 \), we first identify the coefficients and the variables. The coefficients are 7 and -28, and the variables involve \( y^5 \) and \( y^6 \). The greatest common factor of the coefficients is 7, and for the variable part, the common factor is \( y^5 \). Thus, we can factor out \( 7y^5 \) from the expression: \[ 7y^5(1 - 4xy) \] Now, if you were to expand \( 7y^5(1 - 4xy) \), you'd get back the original polynomial. So, the final factored form is: \[ 7y^5(1 - 4xy) \]
