Factorise the following quadratic polynomial by splitting the middle term:
$x^{2}-4x-77$

(A) To factorise the quadratic polynomial $x^{2}-4x-77$,we need to find two numbers whose product is $-77$ and whose sum is $-4$.
$1$. The factors of $-77$ are $(1, -77), (-1, 77), (7, -11), (-7, 11)$.
$2$. Among these,the pair $(7, -11)$ satisfies the condition $7 + (-11) = -4$.
$3$. Now,split the middle term $-4x$ as $7x - 11x$:
$x^{2} + 7x - 11x - 77$
$4$. Group the terms and factor out the common elements:
$x(x + 7) - 11(x + 7)$
$5$. Factor out the common binomial $(x + 7)$:
$(x + 7)(x - 11)$