What is the coefficient?

Question

#(1-x)^21(1+x^2 +x)^20#
find the coefficient of #x^17#

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Answer 1 · 2018-02-20T15:59:12

#0#

The coefficient of #x^17 # is #0# because

#(1-x)^21(1+x^2 +x)^20 = (1-x)^21((x^3-1)/(x-1))^20 = (1-x)(x^3-1)^20#

Now the powers for #x# are #3k# and #3k+1# and as we can verify

#3k=17# or #3k+1=17# does not have integer solution for #k#