Factor out the greatest common factor. \[ -4 p^{3}+32 p^{2}+12 p \]

To factor out the greatest common factor (GCF) from the expression \[ -4 p^{3} + 32 p^{2} + 12 p, \] follow these steps: 1. **Identify the GCF of the coefficients:** - The coefficients are \(-4\), \(32\), and \(12\). - The factors of \(4\) are \(1, 2, 4\). - The factors of \(32\) are \(1, 2, 4, 8, 16, 32\). - The factors of \(12\) are \(1, 2, 3, 4, 6, 12\). - The common factors are \(1, 2, 4\), so the GCF of the coefficients is \(4\). 2. **Identify the GCF of the variables:** - The variables are \(p^3\), \(p^2\), and \(p\). - The smallest exponent of \(p\) is \(1\), so the GCF of the variables is \(p\). 3. **Combine the GCF of the coefficients and variables:** - The overall GCF is \(4p\). 4. **Factor out the GCF from each term:** \[ -4 p^{3} + 32 p^{2} + 12 p = -4p(p^{2} - 8p - 3) \] So, the expression factored by the greatest common factor is: \[ -4p(p^{2} - 8p - 3) \] **Final Answer:** \[ -4\,p\left(p^{2} - 8\,p\,-\,3\,\right) \]