https://file.aiquickdraw.com/mathbot/file/1726082932036lg44342r.jpg

The problem in the image is asking you to factor the trinomial:

\[
2x^2 + 15x + 28
\]

### Step-by-Step Solution:

1. **Multiply the leading coefficient (2) and the constant (28):**
   \[
   2 \times 28 = 56
   \]
2. **Find two numbers that multiply to 56 and add to the middle coefficient (15):**
   \[
   7 \times 8 = 56 \quad \text{and} \quad 7 + 8 = 15
   \]
3. **Rewrite the middle term using these two numbers:**
   \[
   2x^2 + 7x + 8x + 28
   \]
4. **Factor by grouping:**
   Group the terms:
   \[
   (2x^2 + 7x) + (8x + 28)
   \]
   Factor out the greatest common factor (GCF) from each group:
   \[
   x(2x + 7) + 4(2x + 7)
   \]
5. **Factor out the common binomial factor:**
   \[
   (2x + 7)(x + 4)
   \]

Thus, the factored form of \(2x^2 + 15x + 28\) is:
\[
(2x + 7)(x + 4)
\]

Would you like any further details on this method or help with anything else?

---

Here are five follow-up questions for you to consider:
1. Can you factor another trinomial such as \(3x^2 + 11x + 10\) using this method?
2. What happens if the leading coefficient is negative? How does that affect the factoring process?
3. Can you think of a situation where a trinomial is not factorable over the integers?
4. How would you verify the factorization of \(2x^2 + 15x + 28\) by expanding \( (2x + 7)(x + 4) \)?
5. How can you apply factoring trinomials to solving quadratic equations?

**Tip:** Always check your factorization by expanding the factors to ensure you get back the original expression.

Learn how to factor the trinomial 2x^2 + 15x + 28 using the method of factoring by grouping. This tutorial provides a step-by-step breakdown of the solution. Perfect for students in Grades 8-10 looking to improve their algebra skills.

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