1: \(x^2-5x+6=\left(x-2\right)\left(x-3\right)\)
2: \(x^2+5x+6=\left(x+2\right)\left(x+3\right)\)
3: \(x^2-7x+12=\left(x-3\right)\left(x-4\right)\)
4: \(x^2+7x+12=\left(x+3\right)\left(x+4\right)\)
5: \(x^2+x-12=\left(x+4\right)\left(x-3\right)\)
6. x2 - x - 12
<=> x2 - 4x + 3x - 12
<=> x(x - 4) + 3(x - 4)
<=> (x + 3)(x - 4)
7. x2 - 9x + 20
<=> x2 - 4x - 5x + 20
<=> x(x - 4) - 5(x - 4)
<=> (x - 5)(x - 4)
8. x2 + 9x + 20
<=> x2 + 4x + 5x + 20
<=> x(x + 4) + 5(x + 4)
<=> (x + 5)(x + 4)
9. x2 + x - 20
<=> x2 - 4x + 5x - 20
<=> x(x - 4) + 5(x - 4)
<=> (x + 5)(x - 4)
10. x2 - x - 20
<=> x2 - 4x + 5x - 20
<=> x(x - 4) + 5(x - 4)
<=> (x + 5)(x - 4)
11. 2x2 - 3x - 2
<=> 2x2 + x - 4x - 2
<=> x(2x + 1) - 2(2x + 1)
<=> (x - 2)(2x + 1)
12. 3x2 + x - 2
<=> 3x2 + 3x - 2x - 2
<=> 3x(x + 1) - 2(x + 1)
<=> (3x - 2)(x + 1)

