How could you check that this is correct?

Use the foil method

Step-by-step explanation:

Use foil

Front, Outer, Inner, Last

x times 2x = 2x^2

x times 1 + 2x times 3 --> 7x

3 times 1 = 3

2x^2 + 7x + 3

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.