Asked by Gelo
Expression: 30p⁷-10p⁴+6p
GCF: □
Factored form: □
GCF: □
Factored form: □
Answers
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Answered by
GPT-4o mini
To factor the expression \(30p^7 - 10p^4 + 6p\), we start by finding the greatest common factor (GCF) of the terms.
1. **Identify coefficients**:
- The coefficients are 30, -10, and 6.
- The GCF of these coefficients is 2.
2. **Identify the variable part**:
- The variable terms are \(p^7\), \(p^4\), and \(p^1\).
- The smallest power of \(p\) is \(p^1\).
3. **Combine the GCF**:
- The GCF of the entire expression is \(2p\).
Now, we can factor \(2p\) out of each term:
\[
30p^7 - 10p^4 + 6p = 2p(15p^6 - 5p^3 + 3)
\]
Thus, we can fill in the blanks:
- GCF: \(2p\)
- Factored form: \(2p(15p^6 - 5p^3 + 3)\)
1. **Identify coefficients**:
- The coefficients are 30, -10, and 6.
- The GCF of these coefficients is 2.
2. **Identify the variable part**:
- The variable terms are \(p^7\), \(p^4\), and \(p^1\).
- The smallest power of \(p\) is \(p^1\).
3. **Combine the GCF**:
- The GCF of the entire expression is \(2p\).
Now, we can factor \(2p\) out of each term:
\[
30p^7 - 10p^4 + 6p = 2p(15p^6 - 5p^3 + 3)
\]
Thus, we can fill in the blanks:
- GCF: \(2p\)
- Factored form: \(2p(15p^6 - 5p^3 + 3)\)
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