We are asked to factor the quadratic expression $x^2 - 7x - 44$.

1. Problem Description

We are asked to factor the quadratic expression $x^2 - 7x - 44$.

2. Solution Steps

To factor the quadratic $x^2 - 7x - 44$, we need to find two numbers that multiply to $-44$ and add up to $-7$.

Let the two numbers be $a$ and $b$. Then we have:

$a \times b = -44$

$a + b = -7$

The factor pairs of $-44$ are:

$1, -44$

$-1, 44$

$2, -22$

$-2, 22$

$4, -11$

$-4, 11$

The pair $4$ and $-11$ satisfy the conditions since $4 + (-11) = -7$ and $4 \times (-11) = -44$.

Therefore, the factorization is $(x+4)(x-11)$.

$x^2 - 7x - 44 = (x+4)(x-11)$.

3. Final Answer

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