FACTORISE :x4 - 3x2+2

x4-3x2+2=x4-x2-2x2+2 =x2x2-1-2x2-1 =x2-1x2-2 =x2-12x2-22 =x-1x+1x-2x+2 Using identity: a2-b2=a-ba+b⇒x4-3x2+2=x-1x+1x-2x+2

FACTORISE :x⁴ - 3x²+2

x^{4} - 3 x^{2} + 2 = x^{4} - x^{2} - 2 x^{2} + 2 = x^{2} (x^{2} - 1) - 2 (x^{2} - 1) = (x^{2} - 1) (x^{2} - 2) = (x^{2} - 1^{2}) (x^{2} - {(\sqrt{2})}^{2}) = (x - 1) (x + 1) (x - \sqrt{2}) (x + \sqrt{2}) [Using identity : a^{2} - b^{2} = (a - b) (a + b)] \Rightarrow x^{4} - 3 x^{2} + 2 = (x - 1) (x + 1) (x - \sqrt{2}) (x + \sqrt{2})