a: \(x^6+27\)
\(=\left(x^2\right)^3+3^3\)
\(=\left(x^2+3\right)\left(x^4-3x^2+9\right)\)
b: \(x^5+x+1\)
\(=x^5+x^4+x^3-x^4-x^3-x^2+x^2+x+1\)
\(=x^3\left(x^2+x+1\right)-x^2\left(x^2+x+1\right)+\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^3-x^2+1\right)\)
c: \(x^4+2015x^2+2014x+2015\)
\(=x^4+x^3+x^2-x^3-x^2-x+2015x^2+2015x+2015\)
\(=x^2\left(x^2+x+1\right)-x\left(x^2+x+1\right)+2015\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^2-x+2015\right)\)
d: \(x^4+2019x^2+2018x+2019\)
\(=x^4+x^3+x^2-x^3-x^2-x+2019x^2+2019x+2019\)
\(=x^2\left(x^2+x+1\right)-x\left(x^2+x+1\right)+2019\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^2-x+2019\right)\)
