College Algebra - Finding the Coefficient?

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

Answer: -161,700

Update:

Can you explain the steps in solving this?

3 Answers

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  • mizoo
    Lv 7
    2 years ago
    Favorite 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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  • cidyah
    Lv 7
    2 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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  • Anonymous
    2 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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