Question

factor.
$x^2 + 5x + 4$

Explanation:

Step1: Find pair summing to 5, product 4

We need two numbers that add to $5$ and multiply to $4$: $1$ and $4$.

Step2: Split middle term, factor by grouping

$$\begin{align*} x^2 + 5x + 4 &= x^2 + x + 4x + 4\\ &= x(x+1) + 4(x+1) \end{align*}$$

Step3: Factor out common binomial

$$(x+1)(x+4)$$

Answer:

$(x+1)(x+4)$