Question

${x}^{4} + {x}^{2} + 1$
Нужно разложить на множители. Спасите, пожалуйста ​

Answer 1

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

Answer 2

${x}^{4} - {x}^{3} + {x}^{3} + {x}^{2} - {x}^{2} + {x}^{2} + x - x + 1 = {x}^{2} ( {x}^{2} - x + 1) + x( {x}^{2} - x +1 ) + ( {x}^{2} - x + 1) = ( {x}^{2} - x + 1)( {x}^{2} + x + 1)$