Question 252689
I think that the answer to this will be rather long. I shall attempt to answer to satisfaction.
QUESTION #1:How is dividing a polynomial by a binomial similar or different from long division you learned in elementary school?
ANSWER: The technique (steps) are no different than in elementary school. The only difference is that we are using variables.
For example divide 13 by 5.
STEP 1 - you would ask yourself how many times 5 goes into 13 and say 2.
STEP 2 - Place a 2 above the 3 of 13 and multiply 2 x 5 to get 10. Place the 10 below the 13.
STEP 3 - subtract 10 from 13 to get 3. Personally I tell kids "draw the line and change the signs" This helps them remember to change ALL signs.
STEP 4 - write the answer as 2 R3.
Eventually you learned that 2 R 3 became 2 3/5.
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Now, lets take you up one step one the ladder; same problem 13 divided by 5.
STEP #1 - split the 13 onto 10 + 3.
STEP #2 - Now ask yourself how many times 5 goes into 10? you say 2 and place a 2 above the 10.
STEP #3 - multiply 2x5 to get 10, and place the 10 below the 10. Subtract the two to get 0.
STEP #4 - bring down the 3 and repeat. At this point it is sounding like polynomial division. Since 5 can't go into 3, we have 3as a remainder.
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Now we can move up one more step and use variables: 2X + 13 / (x + 5).
STEP #1 - always start with the leading term, the X in this case. Ask yourself X times what get me 2X; you say 2.
STEP #2 - place a 2 above the 2X and then "distribute" the 2 back through the (x + 5) to get 2X + 10.
STEP #3 - place the 2x + 10 below the 2x + 13. Draw the line and change the signs.
STEP #4 - subtract to get only 3. Since X can't go into 3, we are done ad the answer is 2 + 3/(x+5). See how this is similar to elementary remainders?
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QUESTION #2 - Can understanding how to do one kind of division help you with understanding the other kind? 
ANSWER: I hope with the examples above this question is answered.
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QUESTION #3 - What are some examples from real life in which you might uses polynomial division?
ANSWER: Not sure at the moment, but I hope this pretty much gets what you were looking for.