Is There More to Discover about Four Consecutive Numbers?

If the first number is $a$, can you write down the second number in terms of $a$?  How about the third and fourth numbers?

Can you find an expression for the sum of the four consecutive numbers in terms of the first one?

What do all the numbers of the form $2k$ (where $k$ is an integer) have in common?  What about numbers of the form $2k+1$?

In the video below, Claire shows how you could factorise a quartic expression.