\(P=\left(x-1\right)\left(x+2\right)\left(x+4\right)\left(x+7\right)+2069\)
\(=\left[\left(x-1\right)\left(x+7\right)\right]\left[\left(x+2\right)\left(x+4\right)\right]+2069\)
\(=\left(x^2+6x-7\right)\left(x^2+6x+8\right)+2069\)
Đặt \(x^2+6x+2=a\), ta có:
\(P=\left(a-9\right)\left(a+6\right)+2069\)
\(=a^2-3a-54+2069\)
\(=a^2-a+2015\)
=> P chia Q dư 2015