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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 $g(x)$?

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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

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

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
+4795
+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