Factorize trinomials by:
$x^2+(a+b)x+ab = (x+a)(x+b)$:

Got it !

Factorize:

$x^2+5x+6 =$ $x^2+(2+3)x+2 \cdot 3 =(x+2)(x+3) $
$x^2-8x+12 =$
$x^2-4x-5 =$
$x^2+5x-14 =$
$x^3-4x^2-12x =$
$(x^2+16)^2-100x^2 =$
$2x-2-3x+3x^2+x^3-x^2 =$

Simplify by factorizing :

$\frac{x^2-2x-3}{9-x^2} =$
$\frac{x^2-7x-8}{x^3+3x^2+2x} =$
$\frac{x^3-x^2-4x+4}{x^2-3x+2} =$

Solve equations :

$\frac{x}{x^2+x-2}=\frac{1}{1-x}$ $S = \{-1\}$
$\frac{x^2--7x+10}{x^2-25}= \frac{1}{2}$
$\frac{\frac{1}{x-1}}{\frac{1}{-3x+x^2+2}}=-1$