These rumors were spread for the purpose of discrediting the politician's image.

discrediting 是动词 discredit 的现在分词形式。discredit 由前缀 dis-（表示"否定、相反"）和 credit（"信任、信誉"）组成，字面意思是"使失去信誉"，引申为"诋毁、败坏名声"。 在句中 discrediting 表示"通过散布谣言来损害某人声誉"的行为。