If \(f(x)=x^2+2x+5\) and \(g(x)=2x+1\), what is the completed-square form of \((f+g)(x)\)?

Correct answer: \((x+2)^2+2\)

First, \((f+g)(x)=f(x)+g(x)=x^2+2x+5+2x+1=x^2+4x+6\). Completing the square gives \(x^2+4x+6=(x^2+4x+4)+2=(x+2)^2+2\), so option A is correct. Option B would produce the middle term \(-4x\), not \(+4x\). Exam tip: for \(x^2+bx+c\), take half of the coefficient of \(x\), square it, and add and subtract that value.