Answer: 3
Explanation:
The polynomial is:
[tex]2x^2+5x+3[/tex] (1)
We want to factorize it as follows:
[tex](2x+C)(x+1)[/tex]
where C is the unknown number we want to find.
Solving explicitely the last equation,
[tex](2x+C)(x+1)=2x^2 +2x +Cx +C=2x^2 +(2+C)x+C[/tex] (2)
We want eq.(2) to be identical to eq.(1). From the last term, we see immediately that it must be C=3, and 2+C=5. So the missing number is 3, and the factorization is
[tex](2x+3)(x+1)[/tex]
