The given expression is \( 6s^2 + 11s + 4 \).

### To factor this quadratic expression, follow these steps:

1. **Multiply the coefficient of \( s^2 \) (which is 6) and the constant term (which is 4):**
   \[
   6 \times 4 = 24
   \]
2. **Find two numbers that multiply to 24 and add to 11** (the coefficient of \( s \)).
   These numbers are 8 and 3 because:
   \[
   8 \times 3 = 24 \quad \text{and} \quad 8 + 3 = 11
   \]

3. **Rewrite the middle term (11s) using 8 and 3:**
   \[
   6s^2 + 8s + 3s + 4
   \]

4. **Factor by grouping:**
   \[
   (6s^2 + 8s) + (3s + 4)
   \]
   Factor out the greatest common factor (GCF) from each group:
   \[
   2s(3s + 4) + 1(3s + 4)
   \]

5. **Factor out the common binomial factor:**
   \[
   (2s + 1)(3s + 4)
   \]

Thus, the factored form of \( 6s^2 + 11s + 4 \) is:
\[
(2s + 1)(3s + 4)
\]

Would you like more details on any part of the process?

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Here are 5 related questions to practice:

1. How would you factor \( 4s^2 + 12s + 9 \)?
2. What are the solutions to \( (2s + 1)(3s + 4) = 0 \)?
3. Can you expand \( (2s + 1)(3s + 4) \) back into a quadratic?
4. How would you factor \( 6s^2 + 13s + 6 \)?
5. How does factoring help in solving quadratic equations?

**Tip**: Always check if the quadratic can be factored by first finding two numbers that multiply to the product of \( a \times c \) and add to \( b \).

Learn how to factor the quadratic expression 6s^2 + 11s + 4 using the factoring method. This step-by-step guide explores algebraic techniques, including the grouping method and finding factors of a quadratic. Perfect for students in Grades 8-10 looking to understand factoring in detail.

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