If p(x) is any polynomial of degree greater than or equal to 1 and p(x) is divided by the linear polynomial x-a,then the remainder is p(a).

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The Remainder Theorem starts with an unnamed polynomial p(x), where "p(x)" just means "some polynomial p whose variable is x". Then the Theorem talks about dividing that polynomial by some linear factor x – a, where a is just some number. Then, as a result of the long polynomial division, you end up with some polynomial answer q(x) (the "q" standing for "the quotient polynomial") and some polynomial remainder r(x).

Remainder theorem is used to evaluate polynomials such as x for a given value.