The unexpected

Algebra Level 5

Let $f(x)$ be a polynomial of degree 3 such that

when $f(x)$ is divided by $(x-a)$ , the remainder is $a$ ;
when $f(x)$ is divided by $(x-b)$ , the remainder is $b$ ; and
when $f(x)$ is divided by $(x-c)$ , the remainder is $c$ .

Evaluate the remainder when $f(x)$ is divided by $(x-a)(x-b)(x-c)$ .

a

ab +bc +ca

c

b

(a+b+c)

Depends on the values of

x,a,b

and

c

x

2 solutions

Aakash Khandelwal
May 19, 2016

$f(x)= \kappa (x-a) (x-b) (x-c)+x$ .

For all $\kappa \in C$ .

Aditya Kumar
May 6, 2016

Hint: try to interpolate the polynomial by writing it in terms of (x-a), (x-b),(x-c) by using remainder theorem

The unexpected

2 solutions

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