IIT JEE , AIEEE Forum - Mathematics , Algebra

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Degree of polynomial = 1+2+3+.....20 = 210

x⁹ should be dropped from x²¹⁰ so as to get x²⁰¹.

Different combinations in which we can get x⁹ is :

x⁹ = x²x³x⁴
x⁹ = x¹x⁸
x⁹ = x²x⁷
x⁹ = x³x⁶
x⁹ = x⁴x⁵
and x⁹ itself

from the 1st one x⁹ = x²x³x⁴ :

if we multiply variable terms each from (x-1),(x⁵-5),(x⁶-6)......
and constants from (x²-2),(x³-3),(x⁴-4)
we get coefficient of x²¹⁰ for 1st combination which comes out to be (-2)(-3)(-4) = -24

similarly for 2nd combination : x⁹ = x¹x⁸

coefficient is (-1)(-8)

you can evaluate for each combination.

net coefficient comes out to be (-2)(-3)(-4)+(-8)(-1)+(-7)(-2)+(-6)(-3)+(-4)(-5)+(-9)

= 27

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