[tex]a) {x}^{4} - {(1 + \sqrt{2}) }^{2} + \sqrt{2} = \\ \\ {x}^{4} - 1 - 2 \sqrt{2} - { \sqrt{2} }^{2} + \sqrt{2} = \\ \\ {x}^{4} - 1 - 2 \sqrt{2} - 2 + \sqrt{2} = \\ \\ {x}^{4} + ( - 1 - 2) + ( - 2 \sqrt{2} + \sqrt{2}) = \\ \\ {x}^{4} - 3 - \sqrt{2} [/tex]