\(x^3-27x-54\)
\(=x^3-6x^2+6x^2-36x+9x-54\)
\(=x^2\left(x-6\right)+6x\left(x-6\right)+9\left(x-6\right)\)
\(=\left(x-6\right)\left(x^2+6x+9\right)=\left(x-6\right)\left(x+3\right)^2\)
\(4x^3-13x^2+9x-18\)
\(=4x^3-12x^2-x^2+3x+6x-18\)
\(=4x^2\left(x-3\right)-x\left(x-3\right)+6\left(x-3\right)\)
\(=\left(x-3\right)\left(4x^2-x+6\right)\)