Question
Factor out the greatest common factor. If the greatest common factor is 1 , just rety polynomial. \( 16 z^{3}-12 z^{2} \)
Ask by Reid Stewart. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The polynomial \( 16 z^{3} - 12 z^{2} \) factored by the greatest common factor is \( 4 z^{2} (4 z - 3) \).
Solution
To factor out the greatest common factor (GCF) from the polynomial \( 16 z^{3} - 12 z^{2} \):
1. **Identify the GCF of the coefficients:**
- The coefficients are 16 and 12.
- The GCF of 16 and 12 is **4**.
2. **Identify the GCF of the variable parts:**
- The terms are \( z^{3} \) and \( z^{2} \).
- The GCF of \( z^{3} \) and \( z^{2} \) is \( z^{2} \).
3. **Factor out the GCF:**
\[
16 z^{3} - 12 z^{2} = 4 z^{2} (4 z - 3)
\]
**Final Factored Form:**
\[
4 z^{2} (4 z - 3)
\]
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Simplify this solution Extra Insights
The greatest common factor (GCF) of the terms in the polynomial \( 16 z^{3} - 12 z^{2} \) is \( 4z^{2} \). When we factor this out, we simplify the expression to \( 4z^{2}(4z - 3) \). It’s like pulling the best ingredients from a recipe to make the dish even tastier! Factoring polynomials can seem tricky, but it’s all about identifying those common elements. A common mistake is overlooking the variable part. Always ensure you factor out both coefficients and variables to keep everything in balance! There’s a delightful rhythm to factoring once you get the hang of it!
