a. \(x^3-2x^2+x\)
\(=x^3-x^2-x^2+x\)
\(=x^2\left(x-1\right)-x\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2-x\right)\)
\(=\left(x-1\right)x\left(x-1\right)\)
\(=x\left(x-1\right)^2\)
b. \(x^2-2x-15\)
\(=\left(x^2-2x+1\right)-16\)
\(=\left(x-1\right)^2-4^2\)
\(=\left(x-1-4\right)\left(x-1+4\right)\)
\(=\left(x-5\right)\left(x-3\right)\)
c. \(5x^2y^3-25x^3y^4+10x^3y^3\)
\(=5x^2y^3\left(1-5xy+2x\right)\)
d. \(12x^2y-18xy^2-30y^2\)
\(=6y\left(2x^2-3xy-5y\right)\)
e. \(5\left(x-y\right)-y\left(x-y\right)\)
\(=\left(x-y\right)\left(5-y\right)\)
