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11\left(p^{8}-p^{7}+3p^{5}+p^{3}\right)
Factor out 11.
p^{3}\left(p^{5}-p^{4}+3p^{2}+1\right)
Consider p^{8}-p^{7}+3p^{5}+p^{3}. Factor out p^{3}.
11p^{3}\left(p^{5}-p^{4}+3p^{2}+1\right)
Rewrite the complete factored expression. Polynomial p^{5}-p^{4}+3p^{2}+1 is not factored since it does not have any rational roots.