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# College Algebra - Finding the Coefficient?

Find the Coefficient of x^97 in (x-1)^100

Answer: -161,700

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Can you explain the steps in solving this?

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- mizooLv 72 years agoFavorite Answer
(x + y)^n: Coefficient of term x^(n-k) y^k = C(n, k)

x^97: Coefficient of x^(100-3) (-1)^3 is C(100, 3) = 100! / (97! 3!) = 161,700

4th term = C(100, 3) * x^(100-3) (-1)^3 = -161,700x^97

kth term of (x + y)^n = C(n, k-1) x^(n-(k-1)) y^(k-1)

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- cidyahLv 72 years ago
coefficient of x^r is 100C(r-1) x^(r-1) 1^(100-r+1)

r=98

coefficient of x^97 is 100C97 x^97 (-1)^3

100C97 = 100C3

= (100*99*98)/(1*2*3)

= -161700

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- Anonymous2 years ago
Hehe why do they even make you do that stuff? We skipped over that for Calculus, both first and second year. Plus Linear Algebra and every single CS logic courses I've taken. Your math program is weird.

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