*Question*

# Factor \(x^4 + x^2 + 1\)

*Solution:*

Adding and subtracting \(x^2\)

we get , \(x^4 + 2x^2 + 1 – x^2\)

\(= ((x^2)^2 + 2x^2 + 1) – x^2 \)

\( = (x^2 + 1)^2 – x^2\)

\( = (x^2 + 1 + x)(x^2 + 1 – x)\)

Hence, \(x^4 + x^2 + 1 = (x^2 + 1 + x)(x^2 + 1 – x)\)