Answer
The factor of the polynomial ${{x}^{2}}-20x+100$ is ${{\left( x-10 \right)}^{2}}$.
Work Step by Step
${{x}^{2}}-20x+100$
The first and the last terms are perfect squares.
${{x}^{2}}={{\left( x \right)}^{2}}$ and $100={{\left( 10 \right)}^{2}}$
It is a perfect-square trinomial with $A=x$ and $B=10$.
Twice the product of the first and the last terms of the binomial $x+10$ is,
$2\cdot x\cdot \left( 10 \right)=20x$
Therefore, the factorization is,
$\begin{align}
& {{x}^{2}}-20x+100={{x}^{2}}-2\cdot 10\cdot x+{{10}^{2}} \\
& ={{\left( x-10 \right)}^{2}}
\end{align}$
