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The image contains a variety of algebraic factoring problems. I will solve a few selected problems to illustrate the approach for each type of factorization:

### 1. Factor problem from **Exercise 4a**:
Expression:  
\[
6x^2 + 3x - 3
\]
Factor out the greatest common factor (GCF), which is 3:
\[
3(2x^2 + x - 1)
\]
Now factor the quadratic inside the parentheses:
\[
2x^2 + x - 1 = (2x - 1)(x + 1)
\]
Thus, the factored form is:
\[
3(2x - 1)(x + 1)
\]

### 2. Factor problem from **Exercise 6a**:
Expression:
\[
3p^2 - 19pq - 14q^2
\]
Factor the quadratic trinomial:
\[
3p^2 - 19pq - 14q^2 = (3p + 2q)(p - 7q)
\]

### 3. Factor problem from **Exercise 8b**:
Expression:
\[
-15a^2 - 2r^3q + 24r^4
\]
First, factor out the common factor:
\[
-1(15a^2 + 2r^3q - 24r^4)
\]
Now check for any further factorization, but this expression doesn't simplify further through common algebraic factoring techniques.

### 4. Factor problem from **Exercise 9a**:
Expression:
\[
8x^2 + 1 + 2x(x + 1) - 3(x + 1)
\]
Factor by grouping:
\[
(8x^2 + 1) + (2x - 3)(x + 1)
\]

### 5. Factor problem from **Exercise 5a**:
Expression:
\[
z^4 + 6xy + 8y^4
\]
This is a straightforward factoring problem; we will check for factorization based on possible common terms or quadratic forms, but this one seems challenging without using additional algebraic identities.

Would you like further clarification or details on any specific problem or a particular step? Let me know if you have other questions or need me to solve more of these exercises!

Here are 5 related questions for further practice:
1. How do you factor quadratic trinomials in general?
2. What are the steps to factor by grouping?
3. How do you handle factoring when there are negative terms?
4. How can you identify a greatest common factor (GCF) before factoring?
5. What special factorizations should you look for in binomials (e.g., difference of squares)?

**Tip**: Always look for a GCF first before applying more complex factoring techniques.

The user submitted an image containing various algebraic factoring problems.

Explore a range of algebraic factoring problems, from factoring quadratic equations to polynomial expressions. Solutions include step-by-step explanations for factoring using the greatest common factor (GCF), grouping, and factoring quadratics. Ideal for high school students in Grades 9-12.

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