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How is dividing a polynomial by a binomial similar to or different from the long division you learned in elementary school? Can understanding how to do one kind of division help you with understanding the other kind? What are some examples from real life in which you might use polynomial division?

Since this is not my area of expertise, I searched Google under the key words "polynomial binomial division" to get these possible sources:

http://www.sparknotes.com/math/algebra2/polynomials/section2.rhtml
http://www.sparknotes.com/math/algebra2/polynomials/section3.rhtml
http://www.regentsprep.org/regents/math/algebra/AV4/Ldiv.htm
http://en.wikiversity.org/wiki/Synthetic_division

I hope this helps. Thanks for asking.

Take any number (except for 1). Square that number and then subtract one. Divide by one less than your original number. Now subtract your original number. You reached 1 for an answer, didn’t you? How does this number game work? (Hint: Redo the number game using a variable instead of an actual number and rewrite the problem as one rational expression). How did the number game use the skill of simplifying rational expressions? Create your own number game using the rules of algebra and post it for your classmates to solve. Be sure to think about values that may not work. State whether your number game uses the skill of simplifying rational expressions.

Diving a polynomial by a binomial is similar to the long division I learned in elementary school due to the fact you would still set up the long division visual the same. Then you would be dividing the longer number by the small number and the smaller number which would be the polynomial would go on the outside of the visual and the bionomical would be placed in the inside. I do think that understanding how to do long division from the basic steps of math would be very much helpful in understanding how to come up with a solution that would give you an answer to a bionomical expression of division. Using this polynomial division in real life can be associated with trying to understand how long it would take some type of medicine to completely cycle through your body and then in return using it to figure out how long it takes o exit the body completly.

Take any number (except for 1). Square that number and then subtract one. Divide by one less than your original number. Now subtract your original number. You reached 1 for an answer, didn’t you? How does this number game work? (Hint: Redo the number game using a variable instead of an actual number and rewrite the problem as one rational expression). How did the number game use the skill of simplifying rational expressions?
2. Create your own number game using the rules of algebra and post it for your classmates to solve. Be sure to think about values that may not work. State whether your number game uses the skill of simplifying rational expressions.

(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)"

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