Factorise the following quadratic polynomial by splitting the middle term:
$x^{2}+10x+16$

(A) To factorise the quadratic polynomial $x^{2}+10x+16$ by splitting the middle term,we need to find two numbers whose sum is $10$ (the coefficient of $x$) and whose product is $16$ (the constant term).
$1$. Identify the factors of $16$: $(1, 16), (2, 8), (4, 4)$.
$2$. Among these,the pair $(2, 8)$ adds up to $10$.
$3$. Rewrite the middle term $10x$ as $2x + 8x$:
$x^{2} + 2x + 8x + 16$
$4$. Group the terms and factor out the common elements:
$x(x + 2) + 8(x + 2)$
$5$. Factor out the common binomial $(x + 2)$:
$(x + 2)(x + 8)$