Show that x^2 + 4x + 6 cannot be factorised by completing the square.

see explanation

Step-by-step explanation:

Given

x² + 4x + 6

To complete the square

add/subtract (half the coefficient of the x - term) ² to x² + 4x

= x² + 2 (2) x + 4 - 4 + 6

= (x + 2) ² + 2

This does not reduce to a difference of squares and cannot be factored further