SOLUTION: How is dividing a polynomial by a binomial similar or different from long division you learned in elementary school? Can understanding how to do one kind of division help you with

Question 252689: How is dividing a polynomial by a binomial similar or different from 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 uses polynomial division?
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
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.
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