\(f\left(x\right)=\left(x+5\right)\left(x+8\right)\left(x+6\right)\left(x+7\right)+2014\)
\(\Rightarrow f\left(x\right)=\left(x^2+13x+40\right)\left(x^2+13x+42\right)+2014\)
\(\Rightarrow f\left(x\right)=\left(x^2+13x+41-1\right)\left(x^2+13x+41+1\right)+2014\)
\(\Rightarrow f\left(x\right)=\left(x^2+13x+41\right)^2-1+2014=\left(x^2+13x+41\right)^2+2013\)
\(\Rightarrow f\left(x\right)=\left(g\left(x\right)\right)^2+2013\)
\(\Rightarrow f\left(x\right)\) chia \(g\left(x\right)\) dư 2013