Question

What is factor theorem and remainder theorem?​

Answer 1

$\huge\fcolorbox{black}{lime}{AnsweR:}$

Factor Theorem is a special case of Remainder Theorem. Remainder Theorem states that if polynomial ƒ(x) is divided by a linear binomial of the for (x - a) then the remainder will be ƒ(a). Factor Theorem states that if ƒ(a) = 0 in this case, then the binomial (x - a) is a factor of polynomial ƒ(x).

The remainder theorem tells us that for any polynomial f(x) if you divide it by the binomial x−a, the remainder is equal to the value of f(a). The factor theorem tells us that if a is a zero of a polynomial f(x), then (x−a) is a factor of f(x), and vice-versa.

Hope it helps you, dear!❤️❤️❤️

Answer 2

Answer:

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 f(x) has a factor if and only if f(k)=0.

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.