\(A=(x+1)(x+3)(x+5)(x+7)\\=[(x+1)(x+7)][(x+3)(x+5)]\\=(x^2+8x+7)(x^2+8x+15)\\=(x^2+8x+11-4)(x^2+8x+11+4)\\=(x^2+8x+11)^2-16\\=x^4+16x^3+86x^2+176x+105\)
Áp dụng định lý Bezout:
\(R=f(-6)=(-6)^4+16.(-6)^2+86.(-6)^2+176.(-6)+105=-15\ne 0\)
\(→A\not\vdots (x+6)\)