Q2 Consider
$$E = P^2 - 4Q^2 - 3P + 6Q$$
where $P$ and $Q$ are the integral expressions
$$P = 2x^2 - x + 2, \quad Q = x^2 - 2x + 1.$$
(1) By factorizing the right side of $E$, we obtain
$$E = (P - \mathbf{LL}Q)(P + \mathbf{M}Q - \mathbf{MN}).$$
(2) When we express $E$ in terms of $x$, we have
$$E = \mathbf{O}x(x - \mathbf{P})(\mathbf{Q})(\mathbf{Q} - \mathbf{Q}).$$
(3) If $x = -\frac{1 - \sqrt{5}}{3 - \sqrt{5}}$, then the value of $E$ is $\mathbf{S} + \mathbf{T}\sqrt{\mathbf{U}}$.