Un-Distributing Letters

No whole number bigger than 1 divides both terms of ${x}^{2}+7x$. So can it be factored at all?

Yes. Both terms have an $x$. ${x}^{2}$ is $x\cdot x$, and $7x$ is $7\cdot x$. So write one $x$ in front of a bracket:

$${x}^{2}+7x = x\left(x+7\right)$$