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The problem in the image asks to factor the polynomial expression \( x^2 + 15x + 54 \).

To factor this trinomial, we look for two numbers that multiply to give \( 54 \) (the constant term) and add to give \( 15 \) (the coefficient of the middle term).

### Step-by-Step Solution:

1. **Find factors of 54**: 
   - The factors of 54 are: \( 1 \times 54 \), \( 2 \times 27 \), \( 3 \times 18 \), \( 6 \times 9 \).

2. **Choose the correct pair of factors**: 
   - The pair that adds to 15 is \( 6 \) and \( 9 \), because \( 6 + 9 = 15 \) and \( 6 \times 9 = 54 \).

3. **Factor the polynomial**: 
   Using the factors \( 6 \) and \( 9 \), the factored form of \( x^2 + 15x + 54 \) is:
   \[
   (x + 6)(x + 9)
   \]

Thus, the factored form is:
\[
(x + 6)(x + 9)
\]

Do you want more details on this process or have any questions?

### Related Questions:
1. How do you factor polynomials with a leading coefficient other than 1?
2. What method can you use to factor perfect square trinomials?
3. How can the quadratic formula help in factoring polynomials?
4. Can you factor \( x^2 + 15x + 54 \) by grouping? If so, how?
5. How can you verify that your factorization is correct?

### Tip:
Always check your factorization by expanding the factors to ensure you return to the original polynomial.

Factor the polynomial expression x^2 + 15x + 54.

Learn how to factor the quadratic polynomial x^2 + 15x + 54 with a detailed step-by-step solution. This example covers key algebraic concepts like factoring trinomials and quadratic equations, making it suitable for students in Grades 8-10.

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