Question

state remainder theorem and factor theorem​

Answer 1

Answer:

Remainder theorem :-

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.

Factor theorem:-

In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem. The factor theorem states that a polynomial has a factor if and only if.

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Answer 2

$\Large{\underbrace{\sf{Required\:Answer:}}}$

$\large{\underline{\sf{\red{Remainder\:Theorem:}}}}$ It stαtes thαt if p(x) is αny polynomiαl of degree greαter thαn or equαl to one αnd α is αny reαl number, the remαinder obtαined when p(x) is divided by the lineαr polynomiαl (x-α) is p(α).

In other words, when p(x) is divided by (x-α), then the remαinder is given by p(α).

$\large{\underline{\sf{\red{Factor\:Theorem:}}}}$It is α speciαl cαse of remαinder theorem in which remαinder is αlwαys equαl to 0.

According to the fαctor theorem, if (x-α) is α fαctor of α polynomial p(x), then p(α) = 0.

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