Answer
It doesn't factor to that because the original expression is a trinomial (has 3 terms). But in the parentheses, there is only two terms. So, when the expression gets distributed out, there will only be 2 terms. Therefore, the expression cannot factor out to that.
Work Step by Step
If the classmate wanted to make it factor out correctly, they would need to add a +1 after the 3x, inside the parentheses, so there would be 3 terms in the parentheses ( 2($2x^{2}$ + 3x + 1) )and you could distribute it and get the original quadratic expression.
