There are three ways a sentence can be written-
1) Simple sentence- A simple sentence is made up of only one clause. It is made up of a subject, verb and a completed thought.
2) Compound Sentence- A compound sentence consists of two or main clauses which are joined using a coordinating conjunction ( for, and, nor, but, or, yet, so).
3) Complex Sentence - A complex sentence consists of one independent clause and one or more dependent clause. A dependent clause cannot stand alone as a sentence. Therefore, subordinating conjunctions are used before a dependent clause. Some of the most common subordinating conjunctions include after, although, as ,before,while, wherever, whereas,unless, until,though, when, since, even though,if, since, because.
The correct answer is C)Sarah persuaded me to apply for the job. and D)Sarah persuaded me to apply for the job.
Options C and D are correct as the given sentence is a compound sentence and to convert a compound sentence into a simple sentence, we need to reduce one or more main clauses to a word or a phrase (Sarah persuaded me to apply,Sarah persuaded me for applying).
The other options are wrong as and can't be used in a simple sentence.