a) \(x^2-10x+9\)
\(=x^2-9x-x+9\)
\(=x\left(x-9\right)-\left(x-9\right)\)
\(=\left(x-1\right)\left(x-9\right)\)
b) \(3x^2-10xy+3y^2\)
\(=3x^2-9xy-xy+3y^2\)
\(=3x\left(x-3y\right)-y\left(x-3y\right)\)
\(=\left(3x-y\right)\left(x-3y\right)\)
c) \(2x^2-5x+2\)
\(=2x^2-4x-x+2\)
\(=2x\left(x-2\right)-\left(x-2\right)\)
\(=\left(2x-1\right)\left(x-2\right)\)
d) \(2xy-x^2+3y^2-4y+1\)
\(=3xy-xy-x^2+3y^2-3y-y+x-x+1\)
\(=\left(3y^2+3xy-3y\right)-\left(xy+x^2-x\right)-\left(y+x-1\right)\)
\(=3y\left(y+x-1\right)-x\left(y+x-1\right)-\left(y+x-1\right)\)
\(=\left(3y-x-1\right)\left(y+x-1\right)\)
