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)"

Dividing a polynomial by a binomial is similar to long division in elementary school in the sense that it involves a step-by-step process of dividing one number (or expression) by another to find the quotient and remainder. However, there are also key differences between the two.

In elementary school long division, you typically divide a single number (dividend) by another number (divisor) to get the quotient and remainder. On the other hand, dividing a polynomial by a binomial involves dividing a polynomial expression (dividend) by a binomial expression (divisor) to find the quotient and remainder.

To understand polynomial division, it helps to have a solid understanding of long division. The steps involved in long division, such as dividing the digits in order, bringing down the next digit, and subtracting, are similar to the steps involved in polynomial division. However, polynomial division introduces the concept of variable terms and coefficients, which adds an extra layer of complexity.

Understanding long division can provide a foundation for understanding polynomial division. The general process of dividing, subtracting, bringing down, and repeating steps can be applied to both types of division. Additionally, understanding long division can help develop problem-solving skills and the ability to analyze complex mathematical operations, which are important when approaching polynomial division.

As for real-life examples where you might use polynomial division, here are a few:

1. Engineering: In engineering fields, polynomial division can be used to break down complex systems or circuits into simpler components, making it easier to analyze and solve problems.

2. Financial planning: Polynomial division can be used to model investment growth over time. For example, you might use it to calculate compound interest rates or determine the value of investments over a certain period.

3. Data analysis: Polynomial division is used in data fitting and curve fitting techniques. It can help find the best-fit polynomial function to represent a set of data points.

4. Signal processing: Polynomial division is important in various signal processing applications, such as filtering and noise removal. It allows for the manipulation and analysis of complex waveforms.

Overall, understanding polynomial division and its connection to long division can enhance problem-solving skills and help in various domains where complex mathematical operations are involved.