https://file.aiquickdraw.com/mathbot/file/1729562318881ub7ylx54.jpg

The given polynomial is:

\[
18x^3 - 15x^2 + 9x
\]

### Step 1: Identify the Greatest Common Factor (GCF)
The coefficients of the terms are 18, -15, and 9. The GCF of 18, 15, and 9 is **3**.

Next, each term contains a factor of \(x\), and the smallest power of \(x\) is \(x^1\). Therefore, we can factor out \(x\) as well.

Thus, the GCF of the entire polynomial is **3x**.

### Step 2: Factor the Polynomial
Now, divide each term by the GCF \(3x\):

\[
18x^3 ÷ 3x = 6x^2
\]
\[
-15x^2 ÷ 3x = -5x
\]
\[
9x ÷ 3x = 3
\]

### Final Factored Form:
\[
18x^3 - 15x^2 + 9x = 3x(6x^2 - 5x + 3)
\]

This is the factored form of the polynomial.

Do you want more details on any part of the process or have any further questions?

Here are 5 related questions to explore:

1. How do you find the GCF of a set of numbers?
2. Can every polynomial be factored by a GCF?
3. What are the steps to factor a polynomial completely?
4. How does factoring simplify solving polynomial equations?
5. What are the next steps after factoring a polynomial?

**Tip:** Always check if you can factor out a GCF before trying more complex factoring methods!

Factor out the GCF from the given polynomial: 18x^3 - 15x^2 + 9x

Learn how to factor out the greatest common factor (GCF) from the polynomial 18x^3 - 15x^2 + 9x. This solution includes step-by-step guidance on identifying the GCF and factoring polynomials. Suitable for Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation