f: \(x^4-6x^3+12x^2-14x+3\)
\(=x^4-4x^3+x^2-2x^3+8x^2-2x+3x^2-12x+3\)
\(=x^2\left(x^2-4x+1\right)-2x\left(x^2-4x+1\right)+3\left(x^2-4x+1\right)\)
\(=\left(x^2-4x+1\right)\left(x^2-2x+3\right)\)
g: \(2x^4-3x^3-7x^2+6x+8\)
\(=2x^4+2x^3-5x^3-5x^2-2x^2-2x+8x+8\)
\(=2x^3\left(x+1\right)-5x^2\left(x+1\right)-2x\left(x+1\right)+8\left(x+1\right)\)
\(=\left(x+1\right)\left(2x^3-5x^2-2x+8\right)\)
\(=\left(x+1\right)\left(2x^3-4x^2-x^2+2x-4x+8\right)\)
\(=\left(x+1\right)\left\lbrack2x^2\left(x-2\right)-x\left(x-2\right)-4\left(x-2\right)\right\rbrack\)
\(=\left(x+1\right)\left(x-2\right)\left(2x^2-x-4\right)\)
h: \(12x^2+5x-12y^2+12y-10xy-3\)
\(=12x^2+9x-4x-12y^2-18xy+8xy-3+6y-6y\)
\(=\left(12x^2-18xy+9x\right)-\left(4x-6y+3\right)+\left(8xy-12y^2+6y\right)\)
=3x(4x-6y+3)-(4x-6y+3)+2y(4x-6y+3)
=(4x-6y+3)(3x-1+2y)
i: \(2x^4-7x^3+17x^2-20x+14\)
\(=2x^4-4x^3+4x^2-3x^3+6x^2-6x+7x^2-14x+14\)
\(=2x^2\left(x^2-2x+2\right)-3x\left(x^2-2x+2\right)+7\left(x^2-2x+2\right)\)
\(=\left(x^2-2x+2\right)\left(2x^2-3x+7\right)\)
j: \(4x^4+4x^3+5x^2+2x+1\)
\(=4x^4+2x^3+2x^2+2x^3+x^2+x+2x^2+x+1\)
\(=2x^2\left(2x^2+x+1\right)+x\left(2x^2+x+1\right)+\left(2x^2+x+1\right)\)
\(=\left(2x^2+x+1\right)^2\)
k: \(2x^2-7xy+6y^2+9x-13y-5\)
\(=\left(2x^2-7xy+6y^2\right)+10x-15y-x+2y-5\)
\(=\left(2x^2-4xy-3xy+6y^2\right)+5\left(2x-3y\right)-\left(x-2y+5\right)\)
\(=\left(2x-3y\right)\left(x-2y\right)+5\left(2x-3y\right)-\left(x-2y+5\right)\)
=(2x-3y)(x-2y+5)-(x-2y+5)
=(x-2y+5)(2x-3y-1)
