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学校に行く人は学生だ is the plain. So can I use the polite form such as 学校に行きます人は学生です。
Can you modify nouns with polite verbs in the relative clause?
For your specific example, to make the sentence into polite form you would not change the ending of 行く; e.g. 学校に行く人は学生です。 That rule applies to modified nouns. Here are a few more examples.
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