a)
\(x^3-5x^2+6x\\ \Leftrightarrow x\cdot\left(x^2-5x+6\right)\\ \Leftrightarrow x\cdot\left(x^2-2x-3x+6\right)\\ \Leftrightarrow x\cdot\left[x\cdot\left(x-2\right)-3\cdot\left(x-2\right)\right]\\ \Leftrightarrow x\cdot\left(x-3\right)\cdot\left(x-2\right)\)
b)
\(x^2-3xy+2y^2\\ \Leftrightarrow x^2-xy-2xy+2y^2\\ \Leftrightarrow x\cdot\left(x-y\right)-2y\cdot\left(x-y\right)\\ \Leftrightarrow\left(x-2y\right)\cdot\left(x-y\right)\)
c)
\(-4x^2+10x-4\\ \Leftrightarrow-2\cdot\left(2x^2-5x+2\right)\\ \Leftrightarrow-2\cdot\left(2x^2-x-4x+2\right)\\ \Leftrightarrow-2\cdot\left[x\cdot\left(2x-1\right)-2\cdot\left(2x-1\right)\right]\\ \Leftrightarrow-2\cdot\left(x-2\right)\cdot\left(2x-1\right)\)
d)
\(x^3+2x^2y-xy^2-2y^3\\ \Leftrightarrow x^2\cdot\left(x+2y\right)-y^2\cdot\left(x+2y\right)\\ \Leftrightarrow\left(x+2y\right)\cdot\left(x^2-y^2\right)\\ \Leftrightarrow\left(x+2y\right)\cdot\left(x+y\right)\cdot\left(x-y\right)\)
