How to find reducible form using group theory

The reducible representations you work out yourself and are the 'number of unchanged bonds'.
The irreducible representations are found in the Character Table.

C 2v	E	C 2 (z)	v (xz)	v (yz)	Linear functions, rotations	Quadratic functions	Cubic functions
A 1	+1	+1	+1	+1	z	x 2 , y 2 , z 2	z 3 , x 2 z, y 2 z
A 2	+1	+1	-1	-1	R z	xy	xyz
B 1	+1	-1	+1	-1	x, R y	xz	xz 2 , x 3 , xy 2
B 2	+1	-1	-1	+1	y, R x	yz	yz 2 , y 3 , x 2 y

Number of symmetry elements, h = 4
Where h = 4 and R values (for the number of unchanged bonds when a symmetry element is performed) are 2, 0, 2, 0.

Apply to row A 1 :
Numbers in the round brackets indicate ( N x R x I )
1/4[ (1 x 2 x 1) + (1 x 0 x 1) + (1 x 2 x 1) + (1 x 0 x 1) ] = 1/4 x (4) = 1