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### Question 12:
The expression to factor is:
\[
35x^8 + 15x^7 + 55x^5
\]
1. **Look for the Greatest Common Factor (GCF)**:  
   The numerical GCF of 35, 15, and 55 is 5.  
   The variable GCF is the lowest power of \(x\), which is \(x^5\).  

   So, the GCF of the entire expression is \(5x^5\).

2. **Factor out the GCF**:
   \[
   35x^8 + 15x^7 + 55x^5 = 5x^5(7x^3 + 3x^2 + 11)
   \]

Thus, the factored form is:
\[
5x^5(7x^3 + 3x^2 + 11)
\]

### Question 13:
The expression to factor is:
\[
9x^7 + 15x^6 + 33x^4
\]
1. **Find the GCF**:  
   The numerical GCF of 9, 15, and 33 is 3.  
   The variable GCF is \(x^4\).  

   So, the GCF is \(3x^4\).

2. **Factor out the GCF**:
   \[
   9x^7 + 15x^6 + 33x^4 = 3x^4(3x^3 + 5x^2 + 11)
   \]

Thus, the factored form is:
\[
3x^4(3x^3 + 5x^2 + 11)
\]

Would you like further details on these steps or any specific part?

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Here are five follow-up questions you might explore:
1. How do you find the greatest common factor for numerical coefficients?
2. What is the process for factoring out the lowest power of a variable?
3. How would you verify that your factored expression is correct?
4. Can the factored polynomials in the parentheses be factored further?
5. What is the role of exponents when factoring expressions?

**Tip**: Always double-check your factored terms by distributing them back to ensure the original expression is obtained.

Factor the following expressions:
1. 35x^8 + 15x^7 + 55x^5
2. 9x^7 + 15x^6 + 33x^4

Learn how to factor polynomials by extracting the greatest common factor (GCF). This example covers factoring the expressions 35x^8 + 15x^7 + 55x^5 and 9x^7 + 15x^6 + 33x^4 with detailed solutions, suitable for high school students in grades 9-10.

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