Factorize each of the following expressions : `x^4+x^2+1` (ii) `x^4+5x^2+9`

Explanation

(i)`x^4+x^2+1`
`=(x^2 )^2 +2(x^2 )(1)+1^2 −x^2`
`=(x^2 +1)^2 −x^2`
`=(x^2 +1−x)(x^2 +1+x)`

(ii) `x^4+5x^2+9`
`= x^4+ 5x^2 + x^2 + 9- x^2 `
`=x^4 + 6x^2 + 9- x^2 `
`= (x^2 + 3) (x^2 + 3)- x^2 `
`= (x^2 + 3)^2 - x^2 `
`=(x^2 + 3 – x) (x^2 + 3 + x) `
`= (x^2 – x+3) (x^2 + x+3)`