p(1)=36-48-8+16+4=0, so x=1 is a zero.
p(x)=4(9x4-12x3-2x2+4x+1)
Use synthetic division to reduce the quadratic:
1 | 9 -12 -2 4 1
9 9 -3 -5 | -1
9 -3 -5 -1 | 0 = 9x3-3x2-5x-1.
This cubic is zero when x=1 (9-3-5-1=0) so x=1 is a duplicate zero (x-1)2.
So divide by the zero again:
1 ) 9 -3 -5 -1
9 9 6 | 1
9 6 1 | 0 = 9x2+6x+1 = (3x+1)2, so we have a pair of duplicate zeroes: 1 and -⅓.
p(x)=4(x-1)2(3x+1)2.