(x+1)(x+3)(x+5)(x+7) + 2004
= ( x2 + 8x + 7 ) ( x2 + 8x + 15 ) + 2004
đặt x2 + 8x + 1 = a
\(\Rightarrow\)( a + 6 ) ( a + 14 ) + 2004
= a2 + 20a + 84 + 2004
= a2 + 20a + 2088
Ta thấy a2 + 20a \(⋮\)x2 + 8x + 1
\(\Rightarrow\)(x+1)(x+3)(x+5)(x+7) + 2004 chia x2 + 8x + 1 dư 2088