The expression \( x^2 + 4x - 5 \) can be factored as follows:

1. Look for two numbers that multiply to give \( -5 \) (the constant term) and add to give \( 4 \) (the coefficient of the \( x \)-term).
   - The two numbers are \( 5 \) and \( -1 \) because:
     - \( 5 \times (-1) = -5 \)
     - \( 5 + (-1) = 4 \)

2. Rewrite the middle term \( 4x \) as \( 5x - x \):
   \[
   x^2 + 5x - x - 5
   \]

3. Factor by grouping:
   \[
   (x^2 + 5x) - (x + 5)
   \]
   Factor out the common terms:
   \[
   x(x + 5) - 1(x + 5)
   \]

4. Factor out \( (x + 5) \):
   \[
   (x + 5)(x - 1)
   \]

Thus, the factorization of \( x^2 + 4x - 5 \) is:
\[
(x + 5)(x - 1)
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you factor quadratic expressions with other constant terms?
2. Can all quadratic equations be factored like this one?
3. How does completing the square compare to factoring?
4. What if the quadratic equation doesn't factor neatly?
5. How do we solve a factored quadratic equation?

**Tip:** Always check your factorization by expanding it back to ensure it's correct.

Learn how to factor the quadratic equation x² + 4x - 5 with a detailed step-by-step solution. This problem involves factoring by grouping and applying the zero product property. Suitable for students in Grades 8-10.

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