To factor the polynomial \( x^3 + 4x^2 + 4x \), we can follow these steps:

1. **Factor out the greatest common factor (GCF)**:
   The GCF of the terms \( x^3 \), \( 4x^2 \), and \( 4x \) is \( x \). So we can factor \( x \) out of the polynomial:
   \[
   x^3 + 4x^2 + 4x = x(x^2 + 4x + 4)
   \]

2. **Factor the quadratic expression**:
   Next, we need to factor the quadratic expression \( x^2 + 4x + 4 \). We look for two numbers that multiply to \( 4 \) and add to \( 4 \). These numbers are \( 2 \) and \( 2 \), so we can write:
   \[
   x^2 + 4x + 4 = (x + 2)(x + 2) = (x + 2)^2
   \]

3. **Combine the factors**:
   Putting it all together, we get:
   \[
   x^3 + 4x^2 + 4x = x(x^2 + 4x + 4) = x(x + 2)^2
   \]

So, the factored form of \( x^3 + 4x^2 + 4x \) is:
\[
x(x + 2)^2
\]

Would you like more details or have any questions?

Here are 5 more questions you might want to ask:
1. How do you factor a polynomial completely?
2. What are the common factoring techniques used in algebra?
3. Can you explain how to factor trinomials?
4. How do you factor higher-degree polynomials?
5. What are some tips for solving polynomial equations?

**Tip:** Always start factoring by looking for the greatest common factor (GCF) among all terms in the polynomial. This can simplify the expression and make further factoring easier.

Discover how to factor the polynomial x^3 + 4x^2 + 4x into x(x + 2)^2 through detailed steps. This guide explains key algebraic concepts, including GCF and quadratic factoring techniques, perfect for Grades 7-9.

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