Question

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

Answer 1

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.