Question

what is meant by remainder theorem

Answer 1

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REMAINDER THEOREM :

If the polynomial f(x) is divided by x - α then the remainder R is given by f(x) = (x - α) q(x) + R, where q(x) is the quotient and R is a constant (because the degree of the remainder is less than the degree of the divisor x - α).


Putting x = α, f(α) = (α - α)q(α) + R or f(α) = R

When the polynomial f(x) is divided by x - α, the remainder R = f(α) =  value of f(x) when x is α.

Answer 2

Let, p(x) be any polynomial, of degree, greater than or equal to one and , "a" be any real number. If p(x) is divided by (x. - a ) , then , the remainder is equal to p(a).