https://file.aiquickdraw.com/mathbot/file/1727316995821d2y8adcq.jpg

Let's factor each of the two expressions provided in the image step-by-step.

### (5) \( 6m^2 + 54m - 60 \)

1. **Find the greatest common factor (GCF):**
   The GCF of \( 6m^2 \), \( 54m \), and \( -60 \) is 6. Factor out 6 from the entire expression:
   \[
   6(m^2 + 9m - 10)
   \]

2. **Factor the quadratic:**
   Now, factor \( m^2 + 9m - 10 \). We need two numbers that multiply to give \( -10 \) and add to give \( 9 \).
   
   These numbers are \( 10 \) and \( -1 \) because:
   \[
   10 \times (-1) = -10 \quad \text{and} \quad 10 + (-1) = 9
   \]
   
   So, the factorization is:
   \[
   m^2 + 9m - 10 = (m + 10)(m - 1)
   \]

3. **Final factored form:**
   Substituting back, the fully factored form is:
   \[
   6(m + 10)(m - 1)
   \]

---

### (6) \( 4a^2 + 76a + 360 \)

1. **Find the greatest common factor (GCF):**
   The GCF of \( 4a^2 \), \( 76a \), and \( 360 \) is 4. Factor out 4 from the entire expression:
   \[
   4(a^2 + 19a + 90)
   \]

2. **Factor the quadratic:**
   Now, factor \( a^2 + 19a + 90 \). We need two numbers that multiply to give \( 90 \) and add to give \( 19 \).
   
   These numbers are \( 9 \) and \( 10 \) because:
   \[
   9 \times 10 = 90 \quad \text{and} \quad 9 + 10 = 19
   \]
   
   So, the factorization is:
   \[
   a^2 + 19a + 90 = (a + 9)(a + 10)
   \]

3. **Final factored form:**
   Substituting back, the fully factored form is:
   \[
   4(a + 9)(a + 10)
   \]

---

### Summary:
- (5) \( 6m^2 + 54m - 60 \) factors to: \( 6(m + 10)(m - 1) \)
- (6) \( 4a^2 + 76a + 360 \) factors to: \( 4(a + 9)(a + 10) \)

Would you like more details on these steps or have any questions?

Here are 5 related questions for practice:
1. How would you factor \( 12x^2 + 24x - 36 \)?
2. Can you factor \( 3y^2 + 30y + 72 \)?
3. What would be the first step in factoring \( 8p^2 + 64p + 128 \)?
4. How do you factor quadratics with a negative leading coefficient like \( -2x^2 + 8x - 10 \)?
5. What method would you use to factor a trinomial that cannot be easily factored using simple techniques?

**Tip:** Always check for a greatest common factor (GCF) before factoring trinomials!

Factor each completely: (5) 6m^2 + 54m - 60 and (6) 4a^2 + 76a + 360

Learn how to factor quadratic expressions like 6m^2 + 54m - 60 and 4a^2 + 76a + 360. This detailed solution covers the greatest common factor (GCF) and quadratic factoring techniques. Suitable for students in Grades 9-10.

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