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24 April, 10:50

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.)

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  1. 24 April, 13:23
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    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.
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