To factor the expression \(100x + 1000\) completely, we first notice that both terms share a common factor of \(100\).
Factoring out \(100\), we get:
\[ 100(x + 10) \]
So the completely factored expression is:
\[ 100(x + 10) \]
The correct answer from the provided options is:
100(x+10)
(100 times open paren x plus 10 close paren)