Question

Find the remainder when p(x) is divided by (x-1)(x 2)

Answer 1

Answer:

If a polynomial is divided by (x−1) then remainder is 5 and if divided by (x−2) the remainder is 7. What will be the remainder is the polynomial is divided by (x−1)(x−2) ?

As the degree is unknown so we can't write the polynomial with arbitrary coefficients. So we have to assume the polynomial as f(x). Now we can write ...

f(x)=(x−1)g(x)+5

f(x)=(x−2)h(x)+7

Where g(x) & h(x) are some polynomial of x. then I subtract these two equations, but can't go further. Am I going correct? Should I need to use differentiation?

(If you are using some theorem please provide a link so that I can learn that)