Answer
The number to add is $4$.
The factored form is $(x-2)^2$.
Work Step by Step
The given expression is $x^2-4x$.
This is in the form of $x^2-bx$ where $b=4$.
To find the number to add to complete the square, use the formula $\left(\frac{1}{2}b\right)^2$.
$\Rightarrow \left(\frac{1}{2}b\right)^2=\left(\frac{1}{2}\cdot 4\right)^2=2^2=4$
Add $4$ to the given expression.
$=x^2-4x+4$
$=x^2-2\cdot 2 \cdot x+2^2$
Use the special formula $a^2-2ab+b^2=(a-b)^2$ where $a=x$ and $b=2$.
$=(x-2)^2$
Hence, the factored form is $(x-2)^2$.
