Question

If p(x) be a polynomial such that when it is divided from (x-3) gives remainder 5 and when divided by (x-4) gives remainder 7 , then find the remainder when it is divided by (x-3)(x-4).

Answer 1

p(x)=(x-3)=5
=x=5+3
=8_____(1)
p(x)=(x-4)=7
x=7+4
x=11_____(2)
(x-3)(x-4)=x²-4x-3x+12=x²-7x+12
p(8)=8²-7(8)+12___________by(1)
=64-56+12
=20ans
p(11)=11²-7(11)+12____________by(2)
=121-77+12
=56ans