The correct option is
C 10Given that
f(x)=(x+1)5(x+2)a and
g(x)=(x+1)b(x+2)aGiven that LCM of f(x),g(x) is (x+1)a(x+2)b
Observe (x+1) powers in f(x),g(x) , we can see that LCM of 5,b must be a
Observe (x+2) powers in f(x),g(x) , We can see that LCM of a,a must be b
LCM of a,a is a=b
Since a=b , LCM of 5,b is equivalent to LCM of 5,a , Given that it is equal to a
Therefore a must be equal to 5
So the value of a+b=5+5=10
Therefore the correct option is C