Question

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

Explanation:

Step1: Identify $a,b,c$ for $au^2+bu+c$

$a=1,\ b=-3,\ c=-4$

Step2: Find pair with product $ac$, sum $b$

Need two numbers: product $1\times(-4)=-4$, sum $-3$. The numbers are $-4$ and $1$.

Step3: Split middle term, factor by grouping

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

Answer:

$(u-4)(u+1)$