When x^2 – 36 factorise, the answer is (x-6) (x+6)

But x-6 can be factorised further using surds. So , it looks like infinite sequence. Please explain this ?

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Well-written response Bourbaki!

In addition, to answer Dilshanwj’s question, when factors of x^2 -36 are considered (x-6) and (x+6) are the only

irreduciblefactors of it over R (real numbers). By a factor of a polynomial, we mean, a ‘polynomial‘ that divides the given polynomial. Any factorization that you have suggested leads to non-polynomial expressions.~MetaHub Panel of Teachers’ Forum