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

Depends on the values of

x,a,b

and

c

b

(a+b+c)

c

x

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 8 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.