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 $2x^2+5x+3$
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$\color{#0275d8}{x}$ |
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| $\color{#d9534f}{1x}$ |
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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 $3x^2+16x+5$
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$x$ |
╳ |
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| $x$ |
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Therefore, $3x^2+16x+5=$
Factorize $6x^2+13x+6$
Therefore, $6x^2+13x+6=$
Factorize $8x^2+2x-15$
Therefore, $8x^2+2x-15=$
Factorize $-4x^2+19x-12$
Therefore, $-4x^2+19x-12=$