Question
actor out the greatest common factor. If the greatest common factor is 1 , just retype the polynomial. \( 3 n^{3}-6 n^{2} \)
Ask by Delgado Black. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The factored form of \( 3n^{3} - 6n^{2} \) is \( 3n^{2}(n - 2) \).
Solution
To factor out the **greatest common factor (GCF)** from the polynomial \( 3n^{3} - 6n^{2} \), follow these steps:
1. **Identify the GCF of the coefficients and the variables:**
- **Coefficients:** The coefficients are 3 and 6. The GCF of 3 and 6 is **3**.
- **Variables:** The terms have \( n^{3} \) and \( n^{2} \). The GCF for the variables is \( n^{2} \).
Therefore, the GCF of the entire polynomial is \( 3n^{2} \).
2. **Factor out the GCF:**
\[
3n^{3} - 6n^{2} = 3n^{2}(n) - 3n^{2}(2) = 3n^{2}(n - 2)
\]
**Factored Form:**
\[
3n^{2}(n - 2)
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
The greatest common factor (GCF) of \( 3n^{3} \) and \( -6n^{2} \) is \( 3n^{2} \). When we factor out \( 3n^{2} \) from the polynomial, we get: \( 3n^{2}(n - 2) \) Make sure to always check the coefficients and variables for their common factors before deciding what to factor out. In this case, recognizing that both terms share a 3 and at least \( n^{2} \) helped simplify the expression effectively!
