The expression given is \(-4x^3 + 12x^2 + 16x\).

To simplify or factor this expression, we can look for the greatest common factor (GCF) of the terms.

### Step 1: Identify the GCF
The GCF of the coefficients \(-4\), \(12\), and \(16\) is \(4\). Each term also has a factor of \(x\).

### Step 2: Factor out the GCF
We factor out \(4x\) from each term:

\[
-4x^3 + 12x^2 + 16x = 4x(-x^2 + 3x + 4)
\]

So, the factored form of the expression is:

\[
4x(-x^2 + 3x + 4)
\]

Would you like further details or have any questions?

Here are some related questions:

1. How do you factor a quadratic expression like \(-x^2 + 3x + 4\)?
2. What is the significance of factoring in algebra?
3. How do you determine the greatest common factor (GCF)?
4. Can the expression \(-x^2 + 3x + 4\) be factored further?
5. How does factoring help in solving equations?

**Tip:** Always check if there's a common factor in all terms before trying more complex factoring methods.

Learn how to factor the expression –4x^3 + 12x^2 + 16x by identifying and extracting the greatest common factor (GCF). This detailed step-by-step guide covers essential algebraic concepts suitable for students in Grades 8-10.

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