In algebra, the polynomial remainder theorem or little Bézout’s theorem is an application of Euclidean division of polynomials. It states that the remainder of the division of a polynomial by a linear polynomial is equal to. In particular, is a divisor of if and only if a property known as the factor theorem.

is useful for evaluating polynomials at a given value of x, though it might not seem so, at least at first blush. The starts with an unnamed polynomial p(x), where “p(x)” just means “some polynomial p whose variable is x”.

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