The remainder theorem states that when a polynomial p(x) is divided by (x - a), then the remainder = f(a). This can be proved by Euclid's Division Lemma. By using this, if q(x) is the quotient and 'r' is the remainder, then p(x) = q(x) (x - a) + r.
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 f(x) by a linear polynomial {\displaystyle x-r} is equal to {\displaystyle f(r).}
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The remainder theorem states that when a polynomial p(x) is divided by (x - a), then the remainder = f(a). This can be proved by Euclid's Division Lemma. By using this, if q(x) is the quotient and 'r' is the remainder, then p(x) = q(x) (x - a) + r.
Answer:
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 f(x) by a linear polynomial {\displaystyle x-r} is equal to {\displaystyle f(r).}