A monster polynomial

Algebra Level 3

By multiplying out the following term, you get a monster polynomial. ( 4 x 3 − 4 x + 1 ) 2016 ( x 3 − x + 1 ) 2017 (4x^3-4x+1)^{2016} (x^3-x+1)^{2017}

Let S S be the sum of all coefficients. What is the value of S S ?


The answer is 1.

Christoph Pi by Christoph Pi , 23, Austria

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3 solutions

Christoph Pi
May 8, 2016

At first, a solution might be impossible.
But if you want to find out the sum of coefficients, you only have to plug in 1 instead of x.
(4x³-4x+1)^2016 (x³-x+1)^2017
Plug in:
(4-4+1)^2016
(1-1+1)^2017 = 1^2016*1^2017=1

3 Helpful 0 Interesting 0 Brilliant 0 Confused
H Ike
May 18, 2016

Sum of P(x)'s coefficients is equal to P(1)

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Cantdo Math
May 1, 2020

Suppose,we did multiply the polynomials.Then,it is easy to see in order to sum the coefficients we consider x x as it is 1. 1.

So,simply plugging x = 1 x=1 gives us our answer which is 1 \boxed{1} .

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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