+0  
 
0
49
1
avatar

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 $g(x)$?

Guest Nov 22, 2018

Best Answer 

 #1
avatar+3190 
+1

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

 

Now this is some polynomial

 

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

 

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

Rom  Nov 22, 2018
 #1
avatar+3190 
+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

2 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.