Britain intercepted a secret message in 1917 in which germany sought to - mexico improve its economy. -keep russia from re-entering world war i. - the central powers gain land in the united states. -keep the united states from entering world war i.

Britain intercepted a secret message in 1917 in which Germany sought to HELP MEXICO IMPROVE ITS ECONOMY.
In 1917, A German sent message to Mexico, he was asking Mexico to join Germany to fight against USA. Germany promised to help Mexico to recover all the land it has lost to USA if it agree to the plan. The message was intercepted and made public by the USA.

Best  keep the United States from entering World War I.

Explanation:

That maybe seems a counter-intuitive answer, because when the US found out about the Zimmermann Telegram, it drew the US into the war.  But the idea behind the telegram was that Mexico would engage in war with the United States, which would keep US forces and funding occupied on its own continent and prevent them from jumping into the war in Europe.

Here is the decoded text of the telegram sent by German Foreign Secretary Arthur Zimmermann to the German ambassador to Mexico, Heinrich von Eckardt:

We intend to begin on the first of February unrestricted submarine warfare. We shall endeavor in spite of this to keep the United States of America neutral. In the event of this not succeeding, we make Mexico a proposal of alliance on the following basis: make war together, make peace together, generous financial support and an understanding on our part that Mexico is to reconquer the lost territory in Texas, New Mexico, and Arizona. The settlement in detail is left to you. You will inform the President of the above most secretly as soon as the outbreak of war with the United States of America is certain and add the suggestion that he should, on his own initiative, invite Japan to immediate adherence and at the same time mediate between Japan and ourselves. Please call the President's attention to the fact that the ruthless employment of our submarines now offers the prospect of compelling England in a few months to make peace.