To factor the expression $x^2 - 7x - 18$, we’ll go through these steps:

1. Identify the terms in the quadratic expression: $x^2 - 7x - 18$.

2. Set up the factorization: Since this is a quadratic expression of the form $ax^2 + bx + c$, we look for two numbers that multiply to $-18$ and add up to $-7$.

3. Find the factors of -18 that add to -7: These numbers are $-9$ and $2$, since $-9 \times 2 = -18$ and $-9 + 2 = -7$.

4. Write the expression as a product of two binomials: $x^2 - 7x - 18 = (x - 9)(x + 2)$

So, the factored form of the expression $x^2 - 7x - 18$ is: $(x - 9)(x + 2)$

Would you like a detailed breakdown of any step?

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Follow-up Questions

1. How would you factor a quadratic with a positive constant term, such as $x^2 - 7x + 18$?
2. Can you explain why factoring is useful in solving quadratic equations?
3. What if the coefficient of $x^2$ were greater than 1, like $3x^2 - 7x - 18$?
4. How can you verify if a factorization is correct?
5. How does the quadratic formula relate to factoring?

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Tip

When factoring quadratics, always check if the equation can be simplified or if a common factor exists among all terms before starting.