What is remainder theorem? explain how to use remainder thereom and factor theorem for linear polynomial.

Basically the Remainder theorem states that the remainder of dividing a polynomial P (x) by (x - a) is given by P (a).

So for example if we divide x^ 2 - 2x + 7 by x - 2 the remainder will be

2^2 - 2 (2) + 7 = 7 ...

If the remainder is 0 then the divisor will be a factor of the polynomial. This is the Factor Theorem and can be used to test if a given polynomial has a factor x-a.