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

$3x^2+5x+2$
$3x^2-16x+16$

$3x^2-7x+4$
$3x^2+x-2$

$2x^2+5x-42$
$3x^2+19x-72$

$2x^2+19x+42$
$6x^2-13x+2$

$4x^2+15x-4$
$4x^2+9x-9$

$25x^2+15x-4$
$16x^2+8x-3$

$6x^2-25x+25$
$20x^2+67x+56$