Factorize $T = ax^2+bx+c $: Discriminant: $\Delta = b^2 - 4ac$ $\Delta \lt 0 $ impossible! $\Delta = 0 $ : $T = a(x+\frac{b}{2a})^2 $ $\Delta \gt 0$ : $ T =a(x-x_1)(x-x_2)$ with $ x_1 = \frac{-b+\sqrt \Delta}{2a}$ ; $ x_2 =\frac{-b-\sqrt \Delta}{2a} \}$

Go ! Factorize: !

$2x^2 - x - 6 =$	$2(x-\frac{3}{2})(x-2) \;\;\;\;\;\;\;\;(\Delta > 0)$
$2x^2 - 3x +\frac{9}{0} = $	$2(x- \frac{3}{4})^2 \;\;\;\;\;\;\;\; (\Delta = 0) $
$ x^2 +3x +10 =$	$\Delta = -31 \;\;\;\;\;\;\;\;impossible !$
$\LARGE x^2+2x+1 = $	$\LARGE (x + 1)^2 \;\;\;\;\;\;\;\; (\Delta = 0) $
$\LARGE x^2 - x - 2 = $	$\LARGE (x - 2)(x + 1) \;\;\;\;\;\;\;\; (\Delta = 9) $
$\LARGE 2x^2+5x+4 = $	$\LARGE \Delta = -7 \;\;\;\;\;\;\;\; impossible !$