https://file.aiquickdraw.com/mathbot/file/1726082594781xgff4cgg.jpg

The problem on the screen is asking you to factor the quadratic expression:

\[
x^2 - 2x - 8
\]

### Step-by-Step Solution:
1. **Write the quadratic expression**:
   \[
   x^2 - 2x - 8
   \]
   We are looking to factor this into the form \((x + p)(x + q)\), where \(p\) and \(q\) are numbers that satisfy the following conditions:
   - \(p \times q = -8\) (the constant term)
   - \(p + q = -2\) (the coefficient of the middle term, \(x\))

2. **Find two numbers that multiply to \(-8\) and add to \(-2\)**:
   These numbers are \( -4 \) and \( 2 \), because:
   - \((-4) \times 2 = -8\)
   - \((-4) + 2 = -2\)

3. **Factor the expression**:
   Now that we have the two numbers, we can write the factored form as:
   \[
   (x - 4)(x + 2)
   \]

Thus, the factored form of \(x^2 - 2x - 8\) is:
\[
(x - 4)(x + 2)
\]

You can now input this solution into the answer box: **(x - 4)(x + 2)**.

Would you like further details or have any questions?

### Related Questions:
1. How would you factor \(x^2 + 5x + 6\)?
2. How would you factor \(x^2 - 6x + 9\)?
3. How do you factor a quadratic where the leading coefficient is not 1, like \(2x^2 - 3x - 5\)?
4. What is the difference between factoring a quadratic and completing the square?
5. How can you solve a quadratic equation using factoring?

### Tip:
Always check your factors by expanding them back to the original expression to ensure accuracy.

Factor the quadratic expression: x^2 - 2x - 8

Learn how to factor the quadratic expression x^2 - 2x - 8 using the product-sum method. This problem involves algebraic factoring concepts and is suitable for students in Grades 8-10.

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