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