Factor out  the greatest common factor.
minus2p Superscript 3plus16p Superscript 2plus8p

To factor out the greatest common factor (GCF) from the expression \(-2p^3 + 16p^2 + 8p\), follow these steps:

1. **Identify the GCF of the coefficients**: The coefficients are \(-2\), \(16\), and \(8\). The GCF of these numbers is \(2\).

2. **Identify the GCF of the variables**: The variables have powers \(p^3\), \(p^2\), and \(p\). The GCF for the variable \(p\) is \(p\), as it is the smallest power present.

3. **Factor out the GCF**: Multiply the GCF of the coefficients and the variables, which is \(2p\). Now, divide each term of the expression by \(2p\) to factor it out.

\[
\begin{aligned}
-2p^3 + 16p^2 + 8p & = 2p(-p^2 + 8p + 4)
\end{aligned}
\]

So, the expression factored by the greatest common factor is:

\[
2p(-p^2 + 8p + 4)
\]

Would you like more details on any of the steps?

Here are 5 questions related to factoring:

1. What is the greatest common factor (GCF) of two or more terms?
2. How do you determine the GCF of variables in an algebraic expression?
3. What happens when you factor out a negative GCF?
4. How do you factor trinomials after removing the GCF?
5. How can factoring help in solving quadratic equations?

**Tip:** Always check your factored expression by distributing the GCF back to ensure you get the original expression.

Learn how to factor out the greatest common factor (GCF) from the polynomial expression -2p^3 + 16p^2 + 8p. This problem involves identifying the GCF of coefficients and variables, and applying the process of factoring polynomials. Suitable for students in Grades 7-9.

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