5) \(x^3+x^2-3x-27\)
\(=\left(x^3-27\right)+\left(x^2-3x\right)\)
\(=\left(x-3\right)\left(x^2+3x+9\right)+x\left(x-3\right)\)
\(=\left(x-3\right)\left(x^2+4x+9\right)\)
6) \(x^3+x^2-4x-4\)
\(=\left(x^3-4x\right)+\left(x^2-4\right)\)
\(=x\left(x^2-4\right)+\left(x^2-4\right)\)
\(=\left(x+1\right)\left(x^2-4\right)\)
\(=\left(x+1\right)\left(x-2\right)\left(x+2\right)\)
7) \(x^2-9x-9y-y^2\)
\(=\left(x^2-y^2\right)-\left(9x+9y\right)\)
\(=\left(x-y\right)\left(x+y\right)-9\left(x+y\right)\)
\(=\left(x-y-9\right)\left(x+y\right)\)
8) \(y^4-3y^3+3y^2-y\)
\(=y\left(y^3-3y^2+3y-1\right)\)
\(=y\left(y-1\right)^3\)


