The amount of grass seed needed to cover a lawn is proportional to its area. the lawn is rectangular and has an area of 2c^2 + 2c square meters. factor this polynomial to find possible expressions for the length and width of the lawn. (assume the factors are polynomials.)

Our expression
2c^2 + 2c
can also be written this way:
2cc + 2c

Notice that each term has a 2.
If we factor a 2 out of each term we get this,
2(cc + c)

Notice that each term also has at least one c.
Let's factor a c out of each term as well,

2c(c + 1)

Remember that factoring is really a fancy way of dividing. So when you take c out of c, you're not left with nothing. You're dividing c out of itself, leaving you with 1. So hopefully the + 1 makes sense.

We could distribute the 2 back into the brackets and get,
c(2c + 2)

So our dimensions for length and width could be:
c and (2c + 2)
or
2 and (cc + c)
or
2c and (c + 1)

This third one is probably what they're looking for. It is the one which we fully factored: pulling the 2 and c out.