The expression you provided is \( x^2 + 6x - 27 \). To factor this quadratic expression, we need to find two numbers that multiply to \(-27\) (the constant term) and add to \(6\) (the coefficient of the middle term).

Let's break it down:

1. The product we are looking for is \( -27 \).
2. The sum of the two numbers should be \( 6 \).

We need two numbers that multiply to \(-27\) and add to \(6\). These numbers are \(9\) and \(-3\).

So, we can factor the expression as:
\[
x^2 + 6x - 27 = (x + 9)(x - 3)
\]

Thus, the factored form of the quadratic expression \( x^2 + 6x - 27 \) is \((x + 9)(x - 3)\).

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

Here are 5 related questions you might find interesting:
1. How can you verify if a quadratic expression has been factored correctly?
2. What are the roots of the quadratic equation \(x^2 + 6x - 27 = 0\)?
3. How can you factor quadratic expressions that have leading coefficients greater than 1?
4. What does the discriminant of a quadratic equation tell us about its factorization?
5. How do you factor a quadratic trinomial that has no real roots?

**Tip:** After factoring a quadratic expression, you can check your work by expanding the factors back out to ensure they equal the original expression.

Learn how to factor the quadratic expression x^2 + 6x - 27 with a detailed step-by-step solution. This problem covers key algebraic concepts, including quadratic equations and factoring. Suitable for students in Grades 9-10.

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