Question

Expression: 20p⁵-12p³+8p
GCF: □
Factored Form: □

Answer 1

To find the Greatest Common Factor (GCF) and the factored form of the expression \(20p^5 - 12p^3 + 8p\), we can follow these steps:

1. **Identify the coefficients and the powers of \(p\)**:
- The coefficients are \(20\), \(-12\), and \(8\).
- The terms have powers of \(p\): \(p^5\), \(p^3\), and \(p^1\).

2. **Find the GCF of the coefficients**:
- The GCF of \(20\), \(-12\), and \(8\) can be calculated as follows:
- The factors of \(20\) are \(1, 2, 4, 5, 10, 20\).
- The factors of \(12\) are \(1, 2, 3, 4, 6, 12\).
- The factors of \(8\) are \(1, 2, 4, 8\).
- The common factors are \(1, 2, 4\), so the GCF of the coefficients is \(4\).

3. **Find the GCF of the powers of \(p\)**:
- The minimum power of \(p\) among \(p^5\), \(p^3\), and \(p^1\) is \(p^1\) (or just \(p\)).

4. **Combine the GCF of coefficients and \(p\)**:
- The overall GCF is \(4p\).

5. **Factor out the GCF**:
- Now, let's factor \(4p\) out of each term in the expression:
\[
20p^5 - 12p^3 + 8p = 4p(5p^4 - 3p^2 + 2)
\]

Now we can write our final answers:

- **GCF**: \(4p\)
- **Factored Form**: \(4p(5p^4 - 3p^2 + 2)\)