To simplify the expression \(15k^4 + 35k^3 + 20k^2\), we can factor out the greatest common factor (GCF) from all the terms.

### Step-by-step Solution:

1. **Identify the GCF:**
   - The coefficients are 15, 35, and 20.
   - The GCF of 15, 35, and 20 is 5.
   - The variable \(k\) is present in all terms with the lowest power being \(k^2\).

2. **Factor out the GCF:**
   - The GCF of the expression is \(5k^2\).

3. **Rewrite the expression:**
   \[
   15k^4 + 35k^3 + 20k^2 = 5k^2(3k^2 + 7k + 4)
   \]

So, the simplified form of the expression is:

\[
5k^2(3k^2 + 7k + 4)
\]

Would you like further details or have any questions?

### Related Questions:
1. How do you find the greatest common factor (GCF) of a polynomial?
2. What is the next step after factoring the GCF if we want to fully factor the polynomial?
3. How can we solve a quadratic expression like \(3k^2 + 7k + 4\)?
4. What are the applications of factoring in solving equations?
5. How does factoring help simplify algebraic expressions?

**Tip:** Always look for a GCF before attempting to factor more complex polynomials!

Learn how to factor the polynomial 15k^4 + 35k^3 + 20k^2 by extracting the greatest common factor (GCF). This step-by-step solution helps students understand polynomial factorization, including identifying the GCF and rewriting the expression. Suitable for students in Grades 8-10.

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