a: \(2x^2-5x+2\)
\(=2x^2-4x-x+2\)
=2x(x-2)-(x-2)
=(x-2)(2x-1)
c: \(x^8+x^4+1\)
\(=x^8+2x^4+1-x^4\)
\(=\left(x^4+1\right)^2-\left(x^2\right)^2\)
\(=\left(x^4-x^2+1\right)\left(x^4+x^2+1\right)\)
\(=\left(x^4-x^2+1\right)\left(x^4+2x^2+1-x^2\right)\)
\(=\left(x^4-x^2+1\right)\left[\left(x^2+1\right)^2-x^2\right]\)
\(=\left(x^4-x^2+1\right)\left(x^2+1+x\right)\left(x^2+1-x\right)\)
e: \(8x^2-12xy+4y^2-2x-1\)
\(=9x^2-12xy+4y^2-x^2-2x-1\)
\(=\left(9x^2-12xy+4y^2\right)-\left(x^2+2x+1\right)\)
\(=\left(3x-2y\right)^2-\left(x+1\right)^2\)
\(=\left(3x-2y-x-1\right)\left(3x-2y+x+1\right)\)
\(=\left(2x-2y-1\right)\left(4x-2y+1\right)\)
b: \(3x^2-10xy+3y^2\)
\(=3x^2-9xy-xy+3y^2\)
=3x(x-3y)-y(x-3y)
=(x-3y)(3x-y)
d: \(2xy-x^2+3y^2-4y+1\)
\(=2xy-x^2-y^2+4y^2-4y+1\)
\(=\left(4y^2-4y+1\right)-\left(x^2-2xy+y^2\right)\)
\(=\left(2y-1\right)^2-\left(x-y\right)^2\)
\(=\left(2y-1+x-y\right)\left(2y-1-x+y\right)\)
\(=\left(x+y-1\right)\left(-x+3y-1\right)\)
f: \(x^2-10x+9\)
\(=x^2-x-9x+9\)
=x(x-1)-9(x-1)
=(x-1)(x-9)
