Let $f(x)$ be the polynomial \[f(x)=x^7-3x^3+2.\]If $g(x) = f(x + 1)$, what is the sum of the coefficients of $g(x)$?

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Guest Nov 22, 2018

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Best Answer

$g(x) = f(x+1) = (x+1)^7 - 3(x+1)^3 + 2$

Now this is some polynomial

$g(x) = \sum \limits_{k=0}^7~c_k x^k \\ \text{and we can find the sum of the coefficients by simply finding }g(1)$

$g(1) = 2^7 - 3(2^3)+2 = 128 - 24+2 = 106$

Rom Nov 22, 2018

Rom · Answer 1 · 2018-11-22T07:32:55

$g(x) = f(x+1) = (x+1)^7 - 3(x+1)^3 + 2$

Now this is some polynomial

$g(x) = \sum \limits_{k=0}^7~c_k x^k \\ \text{and we can find the sum of the coefficients by simply finding }g(1)$

$g(1) = 2^7 - 3(2^3)+2 = 128 - 24+2 = 106$