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The expression to factor is:

\[
x^2 - 4x - 32
\]

To factor this quadratic expression, we need to find two numbers that multiply to give the constant term (-32) and add up to give the coefficient of the linear term (-4).

1. We start by identifying the numbers:
   - The product must be \(-32\).
   - The sum must be \(-4\).

2. The numbers that satisfy these conditions are \(-8\) and \(4\), because:
   - \((-8) \times 4 = -32\)
   - \((-8) + 4 = -4\)

3. Therefore, the factored form of the quadratic is:

\[
(x - 8)(x + 4)
\]

Thus, the factored expression is:

\[
(x - 8)(x + 4)
\]

Would you like further details on factoring or have any questions?

Here are 5 related questions to explore:
1. How do you factor quadratics when the leading coefficient is not 1?
2. Can all quadratic equations be factored easily?
3. How is factoring quadratics related to solving quadratic equations?
4. What happens if the quadratic has no real factors?
5. How can you check if your factored form is correct?

**Tip:** Always check your factored form by expanding it back to ensure it matches the original expression.

Learn how to factor the quadratic expression x^2 - 4x - 32. This problem involves factoring quadratic equations and the Zero Product Property. Suitable for students in Grades 8-10.

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