Let $f(x)$ be the polynomial \[f(x)=3x^4+5x^2-9x-2.\] If $g(x)$ is equal to the polynomial $f(x-1)$, what is the sum of the coefficients of

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Let $f(x)$ be the polynomial \[f(x)=3x^4+5x^2-9x-2.\] If $g(x)$ is equal to the polynomial $f(x-1)$, what is the sum of the coefficients of $g$?

michaelcai Sep 10, 2017

CPhill · Answer 1 · 2017-09-10T07:26:03

f(x -1) = 3(x-1)^4 + 5(x-1)^2 - 9(x-1) - 2 =

3 (x^4 - 4x^3 + 6x^2 - 4x + 1) + 5(x^2 - 2x + 1) - 9 (x - 1) - 2 =

3x^4 - 12x^3 + 23x^2 - 31x + 15 = g(x)

The sum of the coefficients of g(x) = 3 - 12 + 23 - 31 + 15 = -2