The given expression is \( 6u^2 + 19u + 15 \). This is a quadratic expression, and we can factor it. Here's the step-by-step solution:

### Step 1: Multiply the coefficient of \( u^2 \) by the constant term.
\[
6 \times 15 = 90
\]
We need to find two numbers that multiply to 90 and add up to 19 (the coefficient of \( u \)).

The numbers are 10 and 9 because:
\[
10 \times 9 = 90 \quad \text{and} \quad 10 + 9 = 19
\]

### Step 2: Rewrite the middle term using 10 and 9.
\[
6u^2 + 10u + 9u + 15
\]

### Step 3: Factor by grouping.
Group the terms in pairs:
\[
(6u^2 + 10u) + (9u + 15)
\]

Factor out the greatest common factor from each group:
\[
2u(3u + 5) + 3(3u + 5)
\]

### Step 4: Factor out the common binomial.
\[
(3u + 5)(2u + 3)
\]

Thus, the factored form of \( 6u^2 + 19u + 15 \) is:
\[
(3u + 5)(2u + 3)
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you solve quadratic equations using the quadratic formula?
2. How can you verify the factors of a quadratic equation?
3. What is the general form of a quadratic equation?
4. How do you apply the distributive property to expand factored expressions?
5. What are the different methods to factor a quadratic expression?

**Tip:** Always check your factored expression by multiplying it back to see if you get the original equation!

Learn how to factor the quadratic expression 6u^2 + 19u + 15 through a detailed step-by-step process. This solution covers key algebraic concepts, including factoring quadratics and applying the distributive property. Suitable for students in Grades 8-10.

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