Difference between $p(x)$ and $p(x+2)$

Question

Suppose i have the following polynomial $$p(x)=\sqrt{7}(x-1/2)$$ What would be $$p(x+2)=?$$ I know it might be a simple question but i can not find the answer, any help would be great. Thank you.

Answer 1

For any $z$ we have $$p(z)=\sqrt{7}(z-1/2).$$ Thus when $z$ is $x+2$ we have $$p(x+2)=\sqrt{7}(x+2-1/2) =\sqrt{7}(x+3/2).$$