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divide using dividion algorithm. write answer in form Q+ R/D where the degree of R< the degree of D

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Matthew S. | Statistics, Algebra, Math, Computer Programming TutorStatistics, Algebra, Math, Computer Prog...
4.9 4.9 (21 lesson ratings) (21)

        x  - 6
2x+3 ) 2x2 - 9x - 20
     -(2x2 + 3x)
           -12x - 20
         -(-12x - 18)
                - 2

The solution is x - 6 - 2/(2x+3).


I wanted to put the answer in a formatted way first.  Now I'll talk about how I did this problem. 

First, I started by looking at 2x2.  If I divide this first term by 2x, what do I get?  That answer is x.  So when I multiply x by 2x+3, I get the quantity 2x2 + 3x.  Just like in long division, you subtract this product out, leaving -12x - 20.  -12x goes into 2x -6 times.  Multiply 2x+3 by -6 gives you -12x - 18, which you subtract out leaving -2.  You can't go any further so the remainder is written in fractional form with the divisor as the denominator: -2/(2x+3).  So you final answer is x - 6 - 2/(2x+3).  This satisfies the question, as R has x to the 0th power and D has x to the 1st power, and has been expressed as Q + R/D... quotient plus remainder over divisor.

And I apologize for the grammatical errors.  I can't edit my comment to go back and fix them, only the original posting.  I hope this helps you.