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The expression given in the image is \( x^2 + 15x + 54 \). The problem likely asks for factoring this quadratic equation.

### Factoring \( x^2 + 15x + 54 \):

1. We need to find two numbers that multiply to 54 (the constant term) and add up to 15 (the coefficient of the linear term \( x \)).
2. The pair of numbers that work are 9 and 6, because:
   - \( 9 \times 6 = 54 \)
   - \( 9 + 6 = 15 \)

So, the factorization of \( x^2 + 15x + 54 \) is:

\[
(x + 9)(x + 6)
\]

This means that the quadratic expression can be written as \( (x + 9)(x + 6) \).

Would you like further details on the factoring process or have any other questions?

### Related Questions:
1. How would you factor a quadratic equation if the leading coefficient is not 1?
2. What is the relationship between the roots of a quadratic equation and its factored form?
3. Can all quadratic equations be factored? If not, what methods can be used to solve them?
4. How do you determine the nature of the roots of a quadratic equation using the discriminant?
5. What is the quadratic formula, and how is it derived?

### Tip:
When factoring quadratics, always check if the quadratic can be factored easily by looking for two numbers that multiply to the constant term and add to the coefficient of the linear term. This can save time compared to other methods like completing the square or using the quadratic formula.

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

Learn how to factor the quadratic expression x^2 + 15x + 54 with a detailed step-by-step solution. This example covers key algebraic concepts, including the factoring of quadratic equations and the Zero Product Property. Suitable for students in Grades 7-9.

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