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Expression: -25x³+5x²

GCF: □
Factored Form: □

1 answer

To factor the expression \(-25x^3 + 5x^2\), we first need to find the greatest common factor (GCF) of the two terms.

  1. Identify the coefficients and variables:

    • The coefficients are \(-25\) and \(5\).
    • The variable part is \(x^3\) and \(x^2\).

  2. Find the GCF of the coefficients:

    • The GCF of \(-25\) and \(5\) is \(5\).

  3. Find the GCF of the variable parts:

    • The common variable is \(x\), and the lower power is \(x^2\).

  4. Combine the GCF of the coefficients and variable parts:

    • Therefore, the overall GCF is \(5x^2\).

  5. Factor out the GCF from the original expression: \[ -25x^3 + 5x^2 = 5x^2(-5x + 1) \]

  • GCF: \(5x^2\)
  • Factored Form: \(5x^2(-5x + 1)\)

So, we can summarize:

  • GCF: \(5x^2\)
  • Factored Form: \(5x^2(-5x + 1)\)