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The expression you want to factor is:

\[
x^2 + 6x - 27 = (x - \_)(x + \_)
\]

To factor this quadratic expression, we need two numbers that multiply to give \(-27\) (the constant term) and add to give \(6\) (the coefficient of the linear term).

We look for factors of \(-27\) whose sum is \(6\):
- Factors of \(-27\) include: \((-1, 27), (-3, 9), (-9, 3), (-27, 1)\)

The pair \((-3, 9)\) adds up to \(6\) and multiplies to give \(-27\).

Thus, the factored form is:

\[
x^2 + 6x - 27 = (x - 3)(x + 9)
\]

Let me know if you want further explanation on this.

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Here are 5 related questions to deepen your understanding:

1. How do you factor quadratics when the leading coefficient is not 1?
2. Can you explain how to use the quadratic formula to solve \(x^2 + 6x - 27 = 0\)?
3. How does factoring help in solving quadratic equations?
4. How would you verify the factored form by expanding it?
5. What is the difference between factorizing and completing the square?

**Tip**: When factoring, always check if the product of the two factors equals the constant term and their sum equals the middle term.

Fill in the gaps to factorise this expression: x^2 + 6x - 27 = (x - __)(x + __).

Learn how to factor the quadratic expression x^2 + 6x - 27 step-by-step. This problem involves factoring quadratics and algebraic manipulation. Suitable for students in Grades 7-9.

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