What is the coefficient?

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

1 Answer
Feb 20, 2018

#0#

Explanation:

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#