Question

factorise: x^4+x^2+1​

Answer 1

Answer:

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

Answer:

Given,

x⁴ + x² + 1

= (x²)² + 2(x²)(1) + 1² - x²

= (x²+ 1)² - x²

= ( x² + 1 - x ) ( x² + 1 + x )

Hence , the solution is: ( x² + 1 - x ) ( x² + 1 + x ).