Question
Find the GCF of the terms of the polynomial.
10zSuperscript 5minus30zSuperscript 4plus6zcubed
10zSuperscript 5minus30zSuperscript 4plus6zcubed
Answers
GPT-4o mini
To find the greatest common factor (GCF) of the terms in the polynomial \( 10z^5 - 30z^4 + 6z^3 \), we can follow these steps:
1. **Identify the coefficients**: The coefficients in the terms are 10, -30, and 6.
2. **Find the GCF of the coefficients**:
- The factors of 10 are \( 1, 2, 5, 10 \).
- The factors of 30 are \( 1, 2, 3, 5, 6, 10, 15, 30 \).
- The factors of 6 are \( 1, 2, 3, 6 \).
- The common factors are \( 1, 2 \), and the GCF of the coefficients is \( 2 \).
3. **Identify the variable factor**: The variable parts are \( z^5, z^4, \) and \( z^3 \).
4. **Determine the lowest power of \( z \)**:
- The lowest power among \( z^5, z^4, z^3 \) is \( z^3 \).
5. **Combine GCF of coefficients and variable part**:
- The GCF of the polynomial is \( 2z^3 \).
Therefore, the GCF of the terms of the polynomial \( 10z^5 - 30z^4 + 6z^3 \) is \( \boxed{2z^3} \).
1. **Identify the coefficients**: The coefficients in the terms are 10, -30, and 6.
2. **Find the GCF of the coefficients**:
- The factors of 10 are \( 1, 2, 5, 10 \).
- The factors of 30 are \( 1, 2, 3, 5, 6, 10, 15, 30 \).
- The factors of 6 are \( 1, 2, 3, 6 \).
- The common factors are \( 1, 2 \), and the GCF of the coefficients is \( 2 \).
3. **Identify the variable factor**: The variable parts are \( z^5, z^4, \) and \( z^3 \).
4. **Determine the lowest power of \( z \)**:
- The lowest power among \( z^5, z^4, z^3 \) is \( z^3 \).
5. **Combine GCF of coefficients and variable part**:
- The GCF of the polynomial is \( 2z^3 \).
Therefore, the GCF of the terms of the polynomial \( 10z^5 - 30z^4 + 6z^3 \) is \( \boxed{2z^3} \).