Your answer would be 2x + 1
You can find this by factoring out (x + 4) in the expression 2x² + 9x + 4
First we know that the x-coefficient of the answer must be 2, because you need to end up with 2x². You also know that the number in the answer must be +1, because you need to end up with +4 and you currently have +4, so 4/4 = 1.
Therefore you end up with your answer as 2x + 1
I hope this helps! Let me know if you have any questions :)