Question

Which model represents the factorization of 2x^2+5x+3

Answer 1

`2x^2+5x+3==\left(x+1\right)\left(2x+3\right)`

Explanation:

In order to factorize
`2x^2+5x+3` ,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.

`2x^2+5x+3`

Breaking the middle term

`=\left(2x^2+2x\right)+\left(3x+3\right)`

`2x^2+2x==2x\left(x+1\right)`

`\mathrm{Factor\:out\:}3\mathrm{\:from\:}3x+3\mathrm{:\quad }3\left(x+1\right)`

`2x^2+5x+3=2x\left(x+1\right)+3\left(x+1\right)`

`\mathrm{Factor\:out\:common\:term\:}x+1`

`=\left(x+1\right)\left(2x+3\right)`

Hence

`2x^2+5x+3==\left(x+1\right)\left(2x+3\right)`