Ask a New Question
Menu

Expression: 30p⁷-10p⁴+6p

GCF: □
Factored form: □

1 answer

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: \(2p(15p^6 - 5p^3 + 3)\)