Question
Factor out the greatest common factor. If the greatest common factor is 1 , just retype the polynomial. \( 15 c^{3}+3 c^{2} \) \( 3 c^{2}(5 c+1 \)
Ask by Lewis Barker. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Factor out the greatest common factor: \(3c^2(5c+1)\).
Solution
Factor the expression \( 15c^3+3c^2 \).
Factor the expression by following steps:
- step0: Factor:
\(15c^{3}+3c^{2}\)
- step1: Factor the expression:
\(3\left(5c^{3}+c^{2}\right)\)
- step2: Factor the expression:
\(3c^{2}\left(5c+1\right)\)
The greatest common factor of the polynomial \(15c^3 + 3c^2\) is 3. Factoring out the greatest common factor, we get \(3c^2(5c+1)\).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To factor out the greatest common factor (GCF) from \( 15c^{3} + 3c^{2} \), you first identify the GCF of the coefficients and the variables. Here, the GCF of 15 and 3 is 3, and the common variable factor is \( c^{2} \). So, when you factor 3c² out, you get \( 3c^{2}(5c + 1) \). Now, in terms of real-world application, factoring can be incredibly useful in various fields, especially in areas such as engineering and physics, where you often need to simplify equations or break them down into manageable parts for better analysis. Think of it as breaking a large task into smaller, easier tasks to tackle systematically!
