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factor the common factor out of each expression shown

Let's factor the greatest common factor (GCF) out of each expression from the image:

### 1) \( 12x^3 - 40x^2 - 28 \)

- The GCF of the coefficients \( 12, -40, -28 \) is **4**.
- There is an \( x^2 \) common factor between \( 12x^3 \) and \( -40x^2 \), but not the constant term \( -28 \), so no variable is common across all terms.

Factor out the GCF:
\[
4(3x^3 - 10x^2 - 7)
\]

### 2) \( 18a^4 + 18a + 12 \)

- The GCF of the coefficients \( 18, 18, 12 \) is **6**.
- No variable factor is common in all terms.

Factor out the GCF:
\[
6(3a^4 + 3a + 2)
\]

### 3) \( -40p^4 + 45p^2 - 50p \)

- The GCF of the coefficients \( -40, 45, -50 \) is **5**.
- The common variable factor is \( p \), since all terms have at least one \( p \).

Factor out the GCF:
\[
5p(-8p^3 + 9p - 10)
\]

### 4) \( 5p^2 + 10p - 10 \)

- The GCF of the coefficients \( 5, 10, -10 \) is **5**.
- There is no common variable factor across all terms.

Factor out the GCF:
\[
5(p^2 + 2p - 2)
\]

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Let me know if you need more details on any of these steps!

### Related questions:
1. How can I factor trinomials with no common factors?
2. What happens when a common variable factor is shared across all terms?
3. Can the GCF include negative numbers, and how does that affect the factoring?
4. How do you handle expressions with more than three terms?
5. What’s the next step after factoring out the GCF when solving equations?

### Tip:
Always check for both numerical and variable common factors before factoring any expression!

Factor the common factor out of each expression shown in the image.

Learn how to factor the greatest common factor (GCF) out of polynomial expressions. This problem includes factoring terms like 12x^3 - 40x^2 - 28 and 5p^2 + 10p - 10. Detailed step-by-step solutions for algebra students in Grades 8-10.

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