(x+1)(x+3)(x+5)(x+7)+15=(x^2+4x+3)(x+7)+15=(x^3+9x^2+23x+15)(x+7)+15=x^4+16x^3+86x^2+176x+120=x^4+2x^3+14x^3+28x^2+58x^2+116x+60x+120=x^3(x+2)+14x^2(x+2)+58x(x+2)+60(x+2)=(x+2)(x^3+14x^2+58x+60)=(x+2)(x^3+6x^2+8x^2+48x+10x+60)=(x+2)(x^2(x+6)+8x(x+6)+10(x+6))=(x+2)(x+6)(x^2=8x+10)