Question

factor $x^2 - 7x - 44$

Explanation:

Step1: Find pair for product -44, sum -7

We need two numbers that multiply to $-44$ and add to $-7$. These numbers are $-11$ and $4$, since $(-11)\times4=-44$ and $-11+4=-7$.

Step2: Split middle term and factor

Rewrite the quadratic by splitting the $x$-term, then factor by grouping:

$$\begin{align*} x^2 -7x -44&=x^2 -11x +4x -44\\ &=x(x-11)+4(x-11)\\ &=(x-11)(x+4) \end{align*}$$

Answer:

$(x-11)(x+4)$