$$  $$Practice and apply :Factor each trinomial if it is not factorable .write prime ×²+11×+18

To factor the trinomial $ x^2 + 11x + 18 $, let's follow these steps:

### Step 1: Identify the coefficients
The trinomial is of the form $ ax^2 + bx + c $, where:
- $ a = 1 $ (coefficient of $ x^2 $)
- $ b = 11 $ (coefficient of $ x $)
- $ c = 18 $ (constant term)

### Step 2: Find two numbers that multiply to $ c $ and add to $ b $
We need to find two numbers that multiply to 18 (the constant term $ c $) and add to 11 (the coefficient $ b $).

The two numbers that work are 9 and 2 because:
- $ 9 \times 2 = 18 $
- $ 9 + 2 = 11 $

### Step 3: Write the factorization
Now that we have the numbers 9 and 2, we can factor the trinomial as:
\[ x^2 + 11x + 18 = (x + 9)(x + 2) \]

### Final Answer:
The factorization of the trinomial $ x^2 + 11x + 18 $ is:
\[ (x + 9)(x + 2) \]

This trinomial is factorable and is not prime.

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Would you like more details or have any questions?

Here are 5 relative questions you can practice with:

1. Factor the trinomial: $ x^2 + 12x + 20 $.
2. Determine if the trinomial $ x^2 + 10x + 25 $ is factorable.
3. Factor the expression $ x^2 + 7x + 12 $.
4. Factor the quadratic expression $ x^2 + 14x + 49 $.
5. Is the trinomial $ x^2 + 8x + 15 $ a perfect square?

**Tip:** When factoring trinomials, always check if the middle term can be split into two numbers that satisfy both addition and multiplication conditions.

Learn how to factor the trinomial x^2 + 11x + 18 with a detailed step-by-step guide. This problem covers key algebraic concepts including factoring quadratic trinomials. Suitable for students in Grades 7-9.

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