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Factorizing $ax^2+bx+c$

Factorizing $ax^2+bx+c$

Expand $\left(\color{#0275d8}{2x}+\color{#d9534f}{3}\right)\left(\color{#d9534f}{x}+\color{#0275d8}{1}\right)=$ $x^2+$ $\color{#0275d8}{x}+$ $\color{#d9534f}{x}+$

$=$ $x^2+$ $x+$

So, to factorize $2x^2+5x+3$
$\color{#0275d8}{x}$ ╳
$\color{#d9534f}{1x}$
where if you cross multiply and add, you get the middle term $5x$

Therefore, $2x^2+5x+3=\left(2x+3\right)\left(x+1\right)$

Practice
Factorize $3x^2+16x+5$
$x$ ╳
$x$
Therefore, $3x^2+16x+5=$

Factorize $6x^2+13x+6$
╳ $3$
Therefore, $6x^2+13x+6=$

Factorize $8x^2+2x-15$
╳ $3$
Therefore, $8x^2+2x-15=$

Factorize $-4x^2+19x-12$
╳
$x$
Therefore, $-4x^2+19x-12=$

Factorize:
$2x^2+9x+9$
$2x^2+5x+3$

$3x^2+10x+8$
$3x^2-x-4$

$3x^2-10x+8$
$2x^2-5x+3$

$3x^2-29x+56$
$3x^2-22x-45$

$3x^2+32x+45$
$6x^2-7x+1$

$7x^2+20x-3$
$7x^2+6x-1$

$20x^2+11x-3$
$25x^2-35x+12$

$8x^2-2x-45$
$8x^2+34x+35$