x^2+3x+2)(x^2+11x+30)-12
=(x+1)(x+2)(x+5)(x+6)-12
=[(x+1)(x+6)][(x+2)(x+5)]-12
=[x^2+7x+6][x^2+7x+10]-12
=(x^2+7x)^2+16(x^2+7x)+60-12
=(x^2+7x)^2+16(x^2+7x)+48
=(x^2+7x+4)(x^2+7x+12)
=(x^2+7x+4)(x+3)(x+4)