Question

X⁴+X²+1:factorise this​

Answer 1

Consider x4 + x2 + 1 = (x4 + 2x2 + 1) – x2 = [(x2)2 + 2x2 + 1] – x2 = [x2 + 1]2 – x2 It is in the form of (a2 – b2) = (a + b)(a – b) Hence [x2 + 1]2 – x2 = [x2 + 1 + x] [x2 + 1 – x]

Answer 2

Step-by-step explanation:

$= > {x}^{4} + {x}^{2} + 1 \\ \\ = > {x}^{4} + 2 {x}^{2} + 1 - {x}^{2} \\ \\ = > {( {x}^{2} + 1)}^{2} - {x}^{2}$

Apply the this formula a²-b²=(a-b)(a+b)

$= > {( {x}^{2} + 1 )}^{2} - {x}^{2} \\ \\ = > ( {x}^{2} + 1 +x)( {x}^{2} + 1 -x) \\ \\ = > ( {x}^{2} + x + 1)( {x}^{2} - x + 1)$