Question given:

Attachment 24062

(I think you can click to enlarge it..)

Both the question and solution are highlighter.. But I Don't unnderstand.. My answer would be:

P_{5}(x) = (x-1) + [(x^{2}/2!)(x-1)^{2}] + [(x^{3}/3!)(X-1)^{3}] + [(x^{4}/4!)(X-1)^{4}+ [(x^{5}/5)(x-1)^{5}

Where are all them zeros coming from, and where did the 120 come from D: !

thank you