SOLUTION: Here is a better example: You are putting a fence in your yard to separate your property from your neighbor's. You are planning on putting a garden between your house and the fenc

Question 181427: Here is a better example:
You are putting a fence in your yard to separate your property from your neighbor's. You are planning on putting a garden between your house and the fence. You've already bought the top soil (new dirt) for your garden because it was on sale. You want to use it all and you don't want to buy more because it is not an sale anymore. You have enough to cover an area equal to a^2+4a+5 square feet where a is the thickness (in feet) of the layer of topsoil that you will put down. You want the width of your garden to be 2 more feet than the thickness of the layer of topsoil. What will the length of your garden be in terms of the thickness of the layer of topsoil (a)?
This example uses a^2+4a+5 which cannot be factored, unlike a^2+4a+4 which can be factored into (a+2)^2 which allows for cancellation rather than other polynomial division methods. Also, the variable "a" is defined in this example, unlike the previous one. The only limitation of this method is in not showing how the expression for area was derived. It takes a little longer and requires some creativity, but making actual "real life" examples requires time and creativity.
Found 2 solutions by Mathtut, mathTurtle:
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
Here is a real life example. Say you know that a rectangle has an area of (a^2+4a+4) square inches, and you know that the width is (a+2) inches. You can use long division to determine the length of the box. (Since area = length * width, length = area/width)

Answer by mathTurtle(1) (Show Source): You can put this solution on YOUR website!
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