Ask a New Question
Menu

Expression: 20p⁵-12p³+8p

GCF: □
Factored Form: □

1 answer

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: \(4p(5p^4 - 3p^2 + 2)\)