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

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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:**

$$
-4\,p\left(p^{2} - 8\,p\,-\,3\,\right)
$$
Factor out the greatest common factor $$4p$$ from the expression: $$ -4p(p^2 - 8p - 3) $$

Factor out the greatest common factor.

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