Ans: A
$\begin{array}{rcl}
a(x^2 -x ) + b(x^2 + x) & \equiv & 2x^2 + 4x \\
ax^2 -ax + bx^2 +bx & \equiv & 2x^2 + 4x \\
(a+b)x^2 + ( -a+b)x & \equiv & 2x^2 + 4x
\end{array}$
$\begin{array}{rcl}
a(x^2 -x ) + b(x^2 + x) & \equiv & 2x^2 + 4x \\
ax^2 -ax + bx^2 +bx & \equiv & 2x^2 + 4x \\
(a+b)x^2 + ( -a+b)x & \equiv & 2x^2 + 4x
\end{array}$
By comparing the coefficients of both sides, we have
$\left\{ \begin{array}{ll}
a+b = 2 & \ldots \unicode{x2460} \\
-a+b= 4 & \ldots \unicode{x2461}
\end{array} \right. $
$\unicode{x2460} – \unicode{x2461}$, we have
$\begin{array}{rcl}
2a & = & -2 \\
a & = & -1
\end{array}$
