\(x^2-6x+8=x^2-6x+9-1\)
\(=\left(x-3\right)^2-1=\left(x-3+1\right)\left(x-3-1\right)=\left(x-2\right)\left(x-4\right)\)
\(3x^2-8x+4=3x^2-6x-2x+4\)
\(=3x\left(x-2\right)-2\left(x-2\right)=\left(x-2\right)\left(3x-2\right)\)
\(9x^2+6x-8=\left(3x\right)^2+6x+1-9\)
\(=\left(3x+1\right)^2-9=\left(3x+1+3\right)\left(3x+1-3\right)=\left(3x+4\right)\left(3x-2\right)\)
\(4x^2-4x-3=4x^2-6x+2x-3\)
\(=2x\left(2x-3\right)+\left(2x-3\right)=\left(2x-3\right)\left(2x+1\right)\)
\(x^2-7x+12=x^2-4x-3x+12\)
\(=x\left(x-4\right)-3\left(x-4\right)=\left(x-4\right)\left(x-3\right)\)
\(x^2-5x-14=x^2-7x+2x-14\)
\(=x\left(x-7\right)+2\left(x-7\right)=\left(x-7\right)\left(x+2\right)\)
1) \(x^2-6x+8\)
\(=x^2-2x-4x+8\)
\(=\left(x^2-2x\right)-\left(4x-8\right)\)
\(=x\left(x-2\right)-4\left(x-2\right)\)
\(=\left(x-2\right)\left(x-4\right)\)
2) \(3x^2-8x+4\)
\(=3x^2-2x-6x+4\)
\(=\left(3x^2-2x\right)-\left(6x-4\right)\)
\(=x\left(3x-2\right)-2\left(3x-2\right)\)
\(=\left(3x-2\right)\left(x-2\right)\)
3) \(9\text{}x^2+6x-8\)
\(=9x^2+12x-6x-8\)
\(=\left(9x^2+12x\right)-\left(6x+8\right)\)
\(=3x\left(3x-4\right)-2\left(3x-4\right)\)
\(=\left(3x-4\right)\left(3x-2\right)\)
4) \(4x^2-4x-3\)
\(=4x^2+2x-6x-3\)
\(=\left(4x^2+2x\right)-\left(6x+3\right)\)
\(=2x\left(2x+1\right)-3\left(2x+1\right)\)
\(=\left(2x+1\right)\left(2x-3\right)\)
5) \(x^2-7x+12\)
\(=x^2-3x-4x+12\)
\(=\left(x^2-3x\right)-\left(4x-12\right)\)
\(=x\left(x-3\right)-4\left(x-3\right)\)
\(=\left(x-3\right)\left(x-4\right)\)
6) \(x^2-5x-14\)
\(=x^2+2x-7x-14\)
\(=\left(x^2+2x\right)-\left(7x+14\right)\)
\(=x\left(x+2\right)-7\left(x+2\right)\)
\(=\left(x+2\right)\left(x-7\right)\)
