Question

Factorise x^{2}+5x+6.

Answer 1

x² + 5x +6

⇒x² + (2+3)x + 6

⇒x² + 2x + 3x + 6 

⇒x(x+2) +3(x+2)

⇒(x+3)(x+2)

therefore,

either,        or,

x+3=0        x+2=0 

x=-3           x=-2

Answer 2

x²+5x+6 can be written as :- 
x² + 2x + 3x + 6
= x(x+2) + 3(x+2)
= (x+3)(x+2) [Taking x+2 as common]

Hope that helps !!