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```
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

```
6 years ago

```							since divisor is cubic therefore degree of remaider 2 or less then 2. let remainder be Ax2+Bx+Cp(x)= (x-a)(x-b)(x-c).q(x)+Ax2+Bx+c  [dividend= divisor x quotient + remainder]............1put x=a,b,c in 1p(a)= Aa2+Ba+C or a=Aa2+Ba+C.........2p(b)= Ab2+Bb+C or b= Ab2+Bb+C..............3p(c)=Ac2+Bc+c or c=Ac2+Bc+C.............4subtract equation 2 from 3 & 3 from 4, find the value of A,B and C and get the required answer.Thanks & RegardsSunil RaikwaraskIITiann's faculty
```
6 years ago
```							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
```
6 years ago
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