To factor the quadratic expression \( x^2 - 3x - 40 \), we need to find two numbers that multiply to \(-40\) (the constant term) and add to \(-3\) (the coefficient of \(x\)).

The numbers that fit these criteria are \(5\) and \(-8\) because:

- \(5 \times (-8) = -40\)
- \(5 + (-8) = -3\)

Now, we can factor the expression:

\[
x^2 - 3x - 40 = (x + 5)(x - 8)
\]

Thus, the factored form of the expression is:

\[
(x + 5)(x - 8)
\]

If you need further details or have any questions, feel free to ask! Here are some related questions you might consider:

1. How do you check if the factorization is correct?
2. What other methods can be used to factor quadratic expressions?
3. Can you explain the significance of the coefficients in a quadratic equation?
4. What are the roots of the equation \(x^2 - 3x - 40 = 0\)?
5. How can completing the square help in solving quadratics? 

**Tip:** Always look for two numbers that fit the multiplication and addition requirements when factoring quadratics.

Learn how to factor the quadratic expression x^2 - 3x - 40 by finding two numbers that multiply to -40 and add to -3. Follow a step-by-step solution that simplifies this algebraic problem, suitable for students in Grades 8-10.

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