Question

what is remainder theorem​

Answer 1

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 by a linear polynomial is equal to In particular, is a divisor of if and only if a property known as the factor theorem.

Answer 2

remainder theorem: Let p(x) be any polynomial of degree greater than or equal to one and let a be any real number. If p(x) is divided by the linear polynomial x – a, then the remainder is p(a). Proof : Let p(x) be any polynomial with degree greater than or equal to 1. Suppose that when p(x) is divided by x – a, the quotient is q(x) and the remainder is r(x), i.e.,p(x) = (x – a) q(x) + r(x) Since the degree of x – a is 1 and the degree of r(x) is less than the degree of x – a, the degree of r(x) = 0. This means that r(x) is a constant, say r. So, for every value of x, r(x) = r. Therefore, p(x) = (x – a) q(x) + r In particular, if x = a, this equation gives us p(a) = (a-a) q(a) + r = r which proves the theorm.

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