Copyright © University of Cambridge. All rights reserved.
'Poly Fibs' printed from https://nrich.maths.org/
Use the defining relation for these polynomials to write $P_6$ in
terms of $P_5$ and $P_4$ then in terms of $P_3$ and $P_2$ and the
result follows.
The results for $P_8$ and for $P_{10}$ are proved similarly.