(i) x² + $\dfrac{4}{x^2}$ - 5

(ii) x⁴ + 12x² + 11

(i) Given,

x² + $\dfrac{4}{x^2}$ - 5

$\Rightarrow x^2 + \dfrac{4}{x^2} - 4 - 1\\[1em] \Rightarrow \Big(x^2 + \dfrac{4}{x^2} - 4\Big) - 1^2\\[1em] \Rightarrow \Big[x^2 + \Big(-\dfrac{2}{x}\Big)^2 + 2 \times x \times \Big(-\dfrac{2}{x}\Big) \Big] - 1^2\\[1em] \Rightarrow \Big(x - \dfrac{2}{x}\Big)^2 - 1^2\\[1em] \Rightarrow \Big[\Big(x - \dfrac{2}{x}\Big) - 1\Big]\Big[\Big(x - \dfrac{2}{x}\Big) + 1\Big]\\[1em] \Rightarrow \Big(x - \dfrac{2}{x} - 1\Big)\Big(x - \dfrac{2}{x} + 1\Big).$

Hence, x² + $\dfrac{4}{x^2} - 5 = \Big(x - \dfrac{2}{x} - 1\Big)\Big(x - \dfrac{2}{x} + 1\Big)$

(ii) Given,

⇒ x⁴ + 12x² + 11

⇒ x⁴ + 11x² + x² + 11

⇒ x²(x² + 11) + 1(x² + 11)

⇒ (x² + 11)(x² + 1).

Hence, x⁴ + 12x² + 11 = (x² + 11)(x² + 1).