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.
