The quadratic trinomial given is \(x^2 + 6x + 9\). To factor this trinomial, we'll look for two numbers that multiply to 9 (the constant term) and add to 6 (the coefficient of the linear term).

Let's break it down:

1. The coefficient of \(x^2\) is 1.
2. We need two numbers that multiply to \(9\) and add to \(6\).
   - The numbers \(3\) and \(3\) satisfy these conditions.

So, the quadratic trinomial can be factored as:

\[
x^2 + 6x + 9 = (x + 3)(x + 3) = (x + 3)^2
\]

The trinomial is a perfect square.

Would you like more details on this factorization or have any other questions?

Here are five related questions you might find interesting:

1. How do you factor quadratic trinomials when the leading coefficient is not 1?
2. Can you solve the equation \(x^2 + 6x + 9 = 0\)?
3. What are the roots of the quadratic equation \(x^2 + 6x + 9 = 0\)?
4. How can you complete the square for any quadratic trinomial?
5. What is the quadratic formula, and how does it relate to factoring?

**Tip:** Factoring is often easier when you recognize special forms like perfect square trinomials or the difference of squares.

Learn how to factor the quadratic trinomial x² + 6x + 9 with a detailed step-by-step solution. This problem covers key algebraic concepts, including factoring perfect square trinomials and using the quadratic formula. Suitable for students in Grades 7-9.

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