Question

factor.
$n^2 - 3n - 4$

Explanation:

Step1: Find pair summing to -3, product -4

We need two numbers that add to $-3$ and multiply to $-4$. These numbers are $-4$ and $1$.

Step2: Split middle term and factor

Rewrite the quadratic using the pair, then factor by grouping:

$$\begin{align*} n^2 - 3n - 4 &= n^2 - 4n + n - 4\\ &= n(n-4) + 1(n-4)\\ &= (n-4)(n+1) \end{align*}$$

Answer:

$(n-4)(n+1)$