Let $a x^7+b x^6+c x^5+d x^4+e x^3+f x^2+g x+h=\left|\begin{array}{ccc}(x+1) & \left(x^2+2\right) & \left(x^2+x\right) \\ \left(x^2+x\right) & (x+1) & \left(x^2+2\right) \\ \left(x^2+2\right) & \left(x^2+x\right) & x+1\end{array}\right|$. Then

None of these

By putting x = 0 an both sides of the equation we have

$h=\left|\begin{array}{lll}1 & 2 & 0 \\ 0 & 1 & 2 \\ 2 & 0 & 1\end{array}\right|=9$

Differentiating both sides and then putting x = 0,

we get g = –3

Hence (4) is the correct answer.