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The polynomial given is \( 35x + 7 \).

To factor out the greatest common factor (GCF), we need to identify the largest factor that divides both terms of the polynomial.

- The first term is \( 35x \) and the second term is \( 7 \).
- The GCF of \( 35 \) and \( 7 \) is \( 7 \), as \( 7 \) divides both numbers.

So, we factor out \( 7 \):

\[
35x + 7 = 7(5x + 1)
\]

Thus, the polynomial \( 35x + 7 \) factored by its GCF is:

\[
7(5x + 1)
\]

Would you like further details or have any questions about this? Here are five related questions:

1. How do you determine the GCF of two numbers?
2. What if the polynomial had more than two terms? How would the process change?
3. How can you check that a factorization is correct?
4. What are common mistakes to avoid when factoring polynomials?
5. How would you factor a polynomial where the terms don't have a common factor?

**Tip:** Always double-check your factorization by distributing the factored terms back to ensure you get the original polynomial.

Factor out the GCF from the given polynomial: 35x + 7

Learn how to factor the polynomial 35x + 7 by finding the greatest common factor (GCF). This step-by-step guide covers key algebraic concepts, such as factoring and identifying the GCF. Suitable for students in Grades 6-8.

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