Question

if f of x is a polynomial and a is any real number then x-a divides​

Answer 1

According to remainder theorem: Let p(x) be any polynomial of degree greater than or equal to one and is divided by the linear polynomial x-a where a be any number which would be the divisor and we get the value of x = a, then the remainder is p (a).

So x-a is said to be the factor of that polynomial p(x).f(x)=(x−a)q(x)+r(x)

where q(x) is the quotient when f(x) is divided by x−a and r(x)

The Remainder Theorem says that we can restate the polynomial in terms of the divisor, and then evaluate the polynomial

x=a

hence putting it we get

$$f(a)= 0 \times q(a) + r(a)$$

$$f(a) = r(a)$$

hence the remainder is f(a)