https://file.aiquickdraw.com/mathbot/file/1729788630194v0i3wmfz.jpg

Let's begin by factoring the given polynomial:

The expression is:
\[
x^3 - 3x^2 - 4x
\]

### Step 1: Factor out the greatest common factor (GCF)
The GCF of the terms \(x^3\), \(3x^2\), and \(4x\) is \(x\). Factoring out \(x\) gives:
\[
x(x^2 - 3x - 4)
\]

### Step 2: Factor the quadratic expression \(x^2 - 3x - 4\)
We need two numbers that multiply to \(-4\) and add up to \(-3\). The pair of numbers is \(-4\) and \(1\). Therefore, we can factor the quadratic as:
\[
x^2 - 3x - 4 = (x - 4)(x + 1)
\]

### Final factored form:
\[
x(x - 4)(x + 1)
\]

This matches the structure in the image. So, the complete factored form is:
\[
x(x - 4)(x + 1)
\]

Would you like more details or have any questions about this process?

Here are 5 related questions to explore:
1. How do you determine the greatest common factor (GCF) of a polynomial?
2. Can all polynomials be factored using this method?
3. How do you factor quadratic equations when no obvious factor pair exists?
4. What is the difference between factoring by grouping and factoring quadratics directly?
5. How can you verify that your factored expression is correct?

**Tip:** Always check your factors by multiplying them back together to ensure you return to the original polynomial.

Learn how to factor the polynomial x^3 - 3x^2 - 4x step-by-step. This problem covers key algebraic concepts like factoring out the greatest common factor and factoring quadratic equations. Suitable for students in Grades 8-10.

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