Question
Find the greatest common factor of the terms of the polynomial. \[ 15 x^{4}+9 x^{3} \]
Ask by French Brewer. in the United States
Mar 13,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The greatest common factor is \( 3x^{3} \).
Solution
To find the greatest common factor (GCF) of the terms of the polynomial \( 15 x^{4} + 9 x^{3} \), we will follow these steps:
1. **Identify the coefficients**: The coefficients of the terms are 15 and 9.
2. **Find the GCF of the coefficients**: We need to find the GCF of 15 and 9.
3. **Identify the variable part**: The variable parts of the terms are \( x^{4} \) and \( x^{3} \).
4. **Find the GCF of the variable parts**: The GCF of \( x^{4} \) and \( x^{3} \) is \( x^{3} \).
Now, let's calculate the GCF of the coefficients:
- The factors of 15 are: \( 1, 3, 5, 15 \)
- The factors of 9 are: \( 1, 3, 9 \)
The greatest common factor of 15 and 9 is \( 3 \).
Now, combining the GCF of the coefficients and the variable part, we have:
\[
\text{GCF} = 3x^{3}
\]
Thus, the greatest common factor of the terms of the polynomial \( 15 x^{4} + 9 x^{3} \) is \( \boxed{3x^{3}} \).
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Simplify this solution The Deep Dive
To find the greatest common factor (GCF) of the terms \( 15x^4 \) and \( 9x^3 \), we start by factoring the coefficients and the variables separately. 1. The coefficients: The GCF of 15 and 9 is 3. 2. The variable: The smallest power of \( x \) in the terms is \( x^3 \). Putting it all together, the GCF of \( 15x^4 \) and \( 9x^3 \) is \( 3x^3 \). So, the greatest common factor of the polynomial is \( 3x^3 \).
