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The given expression is:

\[
35x^5 - 21x^2 - 28x
\]

We need to factor out the greatest common factor (GCF) of the terms.

1. **Coefficients:** The numbers are 35, 21, and 28. The greatest common divisor (GCD) of these is 7.

2. **Variables:** The powers of \( x \) are 5, 2, and 1. The lowest power of \( x \) is \( x^1 \), so we can factor out \( x^1 \).

Thus, the greatest common factor is \( 7x \).

### Factoring:

\[
35x^5 - 21x^2 - 28x = 7x(5x^4 - 3x - 4)
\]

### Final answer:

\[
35x^5 - 21x^2 - 28x = 7x(5x^4 - 3x - 4)
\]

Would you like more details on any step, or do you have any other questions?

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Here are 5 follow-up questions to deepen your understanding:

1. How do you find the GCF of numerical coefficients?
2. Why do we factor out the lowest power of a variable?
3. Can you explain the process of factoring polynomials with more complex terms?
4. How would you check the factorization by multiplying back?
5. What are some practical applications of factoring in solving equations?

**Tip:** Always check your factorization by multiplying the factored terms back together to ensure you get the original expression!

Factor out the greatest common factor: 35x^5 - 21x^2 - 28x

Learn how to factor out the greatest common factor from the expression 35x^5 - 21x^2 - 28x. This problem demonstrates key algebraic concepts including factoring polynomials and determining the GCF for both coefficients and variables. Suitable for students in Grades 8-10.

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