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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.
Poly Fibs
Age 16 to 18
Challenge Level 
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.
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