Question

factor $x^2 - 7x - 44$

Explanation:

Step1: Find pair summing to -7, product -44

We need two numbers $a$ and $b$ such that $a+b=-7$ and $a \times b=-44$. The pair is $4$ and $-11$, since $4 + (-11) = -7$ and $4 \times (-11) = -44$.

Step2: Split middle term and factor

Rewrite the quadratic:
$x^2 + 4x - 11x - 44$
Factor by grouping:
$x(x+4) - 11(x+4)$
Factor out $(x+4)$:
$(x+4)(x-11)$

Answer:

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