2011 PuMAC Problems/Algebra Problem A1

Problem

Find the sum of the coefficients of the polynomial $(63x-61)^4$ .

Solution 1

Note that in a polynomial $\sum^{n}_{i=0} a_ix^i$ , $x=1$ gives $\sum^{n}_{i=0} a_i$ , which is the sum of the coefficients. Therefore, the sum of the coefficients of $(63x-61)^4$ is $(63-61)^4 = 2^4 = \boxed{16}$

Solution 2

Expanding, we get $15752961x^4 - 61011468x^3 + 88611894x^2 - 57199212x + 13845841$ . Summing the coefficients, we have $15752961 - 61011468 + 88611894 - 57199212 + 13845841 = \boxed{16}$

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2011 PuMAC Problems/Algebra Problem A1

Contents

Problem

Solution 1

Solution 2