Question

P(x) is a polynomial satisfying P(x+3/2)=P(x) for all values of x. If P(5)=2006, find P(8).

Answer 1

P (x+(3/2))=p (x)

put x=5

p (5+3/2)=p (5)

p (13/2)=p (5)

but we have given p (5)=2006

so,
p(13/2)=p (5)=2006

now,

put x=13/2

p (13/2+3/2)=p (13/2)

p (8)=p (13/2)

because p (13/2)=2006

so, p (8)=p (13/2)=2006

hence,
p (8)=2006


Hope you understand well!