Question

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

Answer 1

see explanation

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