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It appears that you've uploaded an image of a math exercise involving factoring and finding the greatest common divisor (GCD) or highest common factor (HCF). I'll extract the content from the image and help you solve the equations step by step.

Let's get started by listing the visible problems in the image and finding the solutions. I'll then provide explanations for the steps involved in each problem.

Please give me a moment to analyze the image.From the image, I can identify that the task involves factoring polynomials by finding the greatest common divisor (GCD) or common factor. Here’s a breakdown of the first few expressions from the image:

1. **First Expression (a)**: 
   \[
   12x^2 + 8x + 16x
   \]
   Factoring out the greatest common factor (GCF), we see that \(4x\) is common across the terms:
   \[
   4x(3x + 2 + 4)
   \]

2. **Second Expression (b)**:
   \[
   39p^2 - 13p
   \]
   The GCF here is \(13p\), so:
   \[
   13p(3p - 1)
   \]

3. **Third Expression (c)**:
   \[
   a^3b^2 - a^2b^2c
   \]
   The GCF is \(a^2b^2\):
   \[
   a^2b^2(a - c)
   \]

4. **Fourth Expression (d)**:
   \[
   6x^2 - 24x + 18
   \]
   The GCF is \(6\), so:
   \[
   6(x^2 - 4x + 3)
   \]

5. **Fifth Expression (e)**:
   \[
   3x^3y^2 + 9x^2y^3 - 6x^2y^2
   \]
   The GCF is \(3x^2y^2\):
   \[
   3x^2y^2(x + 3y - 2)
   \]

Would you like further details on the remaining expressions or a deeper explanation for any specific step?

Here are 5 related questions to explore:

1. How do you determine the greatest common factor in a polynomial?
2. What strategies can you use to factor trinomials efficiently?
3. How can you factor a quadratic expression with a leading coefficient other than 1?
4. How do factoring and the distributive property relate to each other?
5. Can all polynomials be factored using integers? If not, what methods exist for complex factoring?

**Tip:** When factoring, always check for the greatest common factor first—it simplifies the process significantly!

A math exercise involving factoring and finding the greatest common divisor (GCD) or highest common factor (HCF) from polynomials.

Practice how to factor polynomials and find the greatest common divisor (GCD) for algebraic expressions. This worksheet provides step-by-step factoring solutions for various polynomials, suitable for students in Grades 7-9.

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