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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)