Factor the polynomial using the greatest common factor. \[ x^{2}+3 x \]

Step 1 ：Factor the polynomial \(x^{2}+3 x\) using the greatest common factor.

Step 2 ：The greatest common factor of the terms in the polynomial is \(x\).

Step 3 ：Take out the GCF, \(x\), from each term in the polynomial.

Step 4 ：This results in the factored form of the polynomial: \(x(x+3)\).

Step 5 ：Final Answer: The factored form of the polynomial \(x^{2}+3 x\) is \(\boxed{x(x+3)}\).