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Difference between revisions of "2011 PuMAC Problems/Algebra Problem A1"

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

Revision as of 23:49, 12 March 2023

Problem

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

Solution

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 $(63-61)^4 = 2^4 = \boxed{16}$

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