Question

what is remainder and factor theorem ? proove .​

Answer 1

Reminder theorem and factor theorem :

• Remainder Theorem Proof: Let f(x) be any polynomial with degree greater than or equal to 1. Further suppose that when f(x) is divided by a linear polynomial p(x) = ( x -a), the quotient is q(x) and the remainder is r(x).

Answer 2

Remainder Theorem - Consider that a polynomial after division results in where D is the divisor, Q is the quotient, and R is the remainder. In this case, the polynomial is divided by where k is a constant. This is the divisor, so .

Factor Theorem - Consider a polynomial f(x) which is divided by (x-c), then f(c)=0

Using remainder theorem,

f(x)= (x-c)q(x)+f(c)

f(x) = (x-c)q(x)+0

f(x) = (x-c)q(x)

Therefore, (x-c) is a factor of the polynomial f(x)

Hope it helps❤❤❤