Question

Factor.
x, squared, minus, x, minus, 2
x
2
−x−2

Answer 1

To factor the quadratic expression \( x^2 - x - 2 \), we need to find two numbers that multiply to \(-2\) (the constant term) and add to \(-1\) (the coefficient of the linear term).

The pair of numbers that meets these criteria is \(-2\) and \(1\) because:
- \(-2 \times 1 = -2\)
- \(-2 + 1 = -1\)

Now we can rewrite the expression using these numbers:

\[
x^2 - x - 2 = x^2 - 2x + x - 2
\]

Next, we can group the terms:

\[
= (x^2 - 2x) + (x - 2)
\]

Now, we can factor by grouping:

\[
= x(x - 2) + 1(x - 2)
\]

Now factor out the common term \((x - 2)\):

\[
= (x - 2)(x + 1)
\]

So the factored form of \( x^2 - x - 2 \) is:

\[
(x - 2)(x + 1)
\]