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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 $g(x)$?

 Nov 22, 2018

Best Answer 

 #1
avatar+6097 
+1

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

 

Now this is some polynomial

 

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

 

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

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 Nov 22, 2018
 #1
avatar+6097 
+1
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

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