To factor the expression \( v^2 - v - 2 \), we need to find two numbers that multiply to \(-2\) (the constant term) and add to \(-1\) (the coefficient of the \(v\) term).
The numbers \(-2\) and \(1\) work because:
- \(-2 \times 1 = -2\)
- \(-2 + 1 = -1\)
Using these numbers, we can rewrite the expression:
\[ v^2 - v - 2 = (v - 2)(v + 1) \]
So the factored form of \( v^2 - v - 2 \) is:
\[ (v - 2)(v + 1) \]