Factor out  the greatest common factor.
minus12p Superscript 3plus32p Superscript 2plus20p


To factor out the greatest common factor (GCF) from the expression \(-12p^3 + 32p^2 + 20p\), follow these steps:

1. **Identify the GCF of the coefficients**: The coefficients are \(-12\), \(32\), and \(20\). The GCF of these numbers is \(4\).

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 \(4p\). Now, divide each term of the expression by \(4p\) to factor it out.

\[
\begin{aligned}
-12p^3 + 32p^2 + 20p & = 4p(-3p^2 + 8p + 5)
\end{aligned}
\]

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

\[
4p(-3p^2 + 8p + 5)
\]

Would you like more details on any of the steps?

Here are 5 questions related to factoring:

1. How do you find the GCF of more complex algebraic expressions?
2. What is the significance of factoring in simplifying expressions?
3. How does the sign of the leading coefficient affect the factored form?
4. Can you factor a quadratic expression completely after removing the GCF?
5. What role does factoring play in solving polynomial equations?

**Tip:** After factoring out the GCF, you can further analyze the remaining polynomial to see if it can be factored further.

Learn how to factor out the greatest common factor from the expression -12p^3 + 32p^2 + 20p. This problem covers algebraic concepts related to factoring polynomials and simplifying expressions. Suitable for high school students studying algebra and polynomial functions.

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