Answer:
[tex]2x^2+5x+3==\left(x+1\right)\left(2x+3\right)[/tex]
Step-by-step explanation:
In order to factorize [tex]2x^2+5x+3[/tex] ,we first need to find the factors of 2 x 3 = 6 such that their sum is 5. 2 and 3 are such factors Hence we can now break the middle term.
[tex]2x^2+5x+3[/tex]
Breaking the middle term
[tex]=\left(2x^2+2x\right)+\left(3x+3\right)[/tex]
[tex]2x^2+2x==2x\left(x+1\right)[/tex]
[tex]\mathrm{Factor\:out\:}3\mathrm{\:from\:}3x+3\mathrm{:\quad }3\left(x+1\right)[/tex]
[tex]2x^2+5x+3=2x\left(x+1\right)+3\left(x+1\right)[/tex]
[tex]\mathrm{Factor\:out\:common\:term\:}x+1[/tex]
[tex]=\left(x+1\right)\left(2x+3\right)[/tex]
Hence
[tex]2x^2+5x+3==\left(x+1\right)\left(2x+3\right)[/tex]
