To fully factor the expression \(-4x^2 + 24x\), follow these steps:

### Step 1: Factor out the greatest common factor (GCF)
The GCF of \(-4x^2\) and \(24x\) is \(-4x\), because both terms have an \(x\) and are divisible by \(-4\). 

So, factor out \(-4x\):
\[
-4x(x - 6)
\]

Thus, the fully factored form of the expression is:
\[
-4x(x - 6)
\]

Would you like a detailed explanation of factoring, or do you have any questions?

Here are 5 related questions:
1. How do you find the greatest common factor of two terms?
2. Can you factor the expression \(6x^2 - 18x\)?
3. How do you factor quadratic expressions like \(x^2 + 5x + 6\)?
4. What happens if the expression has three terms instead of two?
5. How can you check if your factorization is correct?

**Tip:** Always look for the greatest common factor before trying other factoring methods, as it simplifies the problem.

Learn how to fully factor the polynomial -4x^2 + 24x with this detailed guide. This problem covers key algebraic concepts such as factoring and finding the greatest common factor (GCF). Perfect for students in Grades 8-10 studying polynomial expressions.

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