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

EXAMPLE

Let {\displaystyle f(x)=x^{3}-12x^{2}-42}. Polynomial division of {\displaystyle f(x)}by {\displaystyle (x-3)gives the quotient {\displaystyle x^{2}-9x-27}and the remainder {\displaystyle -123} Therefore, {\displaystyle f(3)=-123}.

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Answer 2

ANSWER :

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.

Factor Theorem : . x – a is a factor of the polynomial p(x), if p(a) = 0. Also, if x – a is afactor of p(x), then p(a) = 0, where a is any real number.