A certain polynomial P(x),x E R WHEN DIVIDED BY (x-a),(x-b) and (x-c) leaves remainder a,b,c.then find the remainder when P(x) is divided by (x-a)(x-b)(x-c) where a,b,c are distinct

since divisor is cubic therefore degree of remaider 2 or less then 2. let remainder be Ax²+Bx+C

Consider the cubic polynomial Q(x) = P(x) - x. This polynomial has its roots as a,b,c. Hence P(x) - x = (x-a)(x-b)(x-c) R(x) for some polynomial R(x). Hence P(x) = (x-a)(x-b)(x-c) R(x)+x We can immediately see that the remainder when P(x) is divided by (x-a)(x-b)(x-c) is x