Question

Define remainder and factor theorem in simple languages...

Answer 1

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: if p(x) be any polynomial and if p(x) is divided by the linear polynomial x-a, then the remainder is p(a). for example: if p(x)=x^3+ 3x^2+3x+1 is divided by x+1, then the remainder will be: x+1=0
x=-1
p(-1)= (-1)^3+3*(-1)^2+3*(-1)+1
= -1+3+(-3)+1
=-1+3-3+1
= 0
so by remainder theorem 0 is remainder of polynomial p(x).
factor theorem : if p(x) is a polynomial and a is any real number then
:x-a is a factor of p(x), if p(a)=0,and p(a)=0, if x-a is a factor of p(x).

hope it will help you!