Answer:
(2x+3)(x+1)
Step-by-step explanation:
The given trinomial is:
[tex]2 {x}^{2} + 5x + 3[/tex]
This trinomial is of the form:
[tex]a {x}^{2} + bx + c[/tex]
where a=2, b=5, c=3
We multiply a by c to get
ac=6
Two factors of 6 that sums up to 5 are 2 and 3.
Split the middle term with these factors to get:
[tex]2 {x}^{2} + 2x + 3x + 3[/tex]
Factor by grouping
[tex]2x(x + 1) + 3(x + 1)[/tex]
[tex](2x + 3)(x + 1)[/tex]
