Factor.
x squared minus 2 x minus 48x2−2x−48

To factor the quadratic expression \(x^2 - 2x - 48\), we need to find two numbers that multiply to \(-48\) and add to \(-2\).

Let's proceed step-by-step:

1. We are looking for factors of \(-48\) whose sum is \(-2\).
2. The numbers that satisfy this are \(6\) and \(-8\), because:

\[
6 \times (-8) = -48 \quad \text{and} \quad 6 + (-8) = -2
\]

3. Now, we can rewrite the middle term \(-2x\) as \(6x - 8x\):

\[
x^2 - 2x - 48 = x^2 + 6x - 8x - 48
\]

4. Now, group the terms:

\[
(x^2 + 6x) - (8x + 48)
\]

5. Factor each group:

\[
x(x + 6) - 8(x + 6)
\]

6. Finally, factor out the common term \((x + 6)\):

\[
(x - 8)(x + 6)
\]

Thus, the factored form of the quadratic expression \(x^2 - 2x - 48\) is:

\[
(x - 8)(x + 6)
\]

Would you like more details or have any further questions?

Here are five related questions for practice:
1. How would you factor \(x^2 + 5x + 6\)?
2. What is the factored form of \(x^2 - 9x + 20\)?
3. How do you factor \(x^2 - 16\)?
4. What is the difference between factoring and expanding?
5. Can every quadratic equation be factored using integers?

**Tip**: When factoring, always look for pairs of numbers that multiply to the constant term and add up to the middle coefficient.

Learn how to factor the quadratic expression x^2 - 2x - 48 using a step-by-step approach. This problem involves factoring methods for quadratic equations, targeting algebra concepts. Suitable for students in Grades 8-10.

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