SOLUTION: Divide using long division: {{{(-2x^3+x^2-2x+3)/(x+2)}}}

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Question 687541: Divide using long division:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!



 Write this:

                           
x + 2)-2x³ +  x² -  2x +  3

      
-2x³ divided by x give -2x².  Write that above the + x²

            -2x²           
x + 2)-2x³ +  x² -  2x +  3
      
     
-2x² times +2 gives -4x².  Write that under the + x²

            -2x²           
x + 2)-2x³ +  x² -  2x +  3
           - 4x²


-2x² times x gives -2x³.  Write that under the -2x³:

            -2x²           
x + 2)-2x³ +  x² -  2x +  3
      -2x³ - 4x²
            

Draw a line:

            -2x²           
x + 2)-2x³ +  x² -  2x +  3
      -2x³ - 4x²
             
     
Subtract -2x³ - (-2x³), that gives 0 so we don't write anything
under that.  then x² minus -x² is really x²+4x² or 5x²

            -2x²           
x + 2)-2x³ +  x² -  2x +  3
      -2x³ - 4x²
             5x²  

Bring down the - 2x

            -2x²           
x + 2)-2x³ +  x² -  2x +  3
      -2x³ - 4x²
             5x² -  2x
             


5x² divided by x gives + 5x.  Write that at the top after -2x²

            -2x² +  5x     
x + 2)-2x³ +  x² -  2x +  3
      -2x³ - 4x²
             5x² -  2x
           


5x times + 2 gives + 10x.  Write that under the - 2x

            -2x² +  5x     
x + 2)-2x³ +  x² -  2x +  3
      -2x³ - 4x²
             5x² -  2x
                 + 10x

5x times x gives 5x².  Write that under the 5x²

            -2x² +  5x - 12
x + 2)-2x³ +  x² -  2x +  3
      -2x³ - 4x²
             5x² -  2x
             5x² + 10x
                   

Draw a line:

            -2x² +  5x - 12
x + 2)-2x³ +  x² -  2x +  3
      -2x³ - 4x²
             5x² -  2x
             5x² + 10x
                  

Subtract 5x² - 5x², that gives 0 so we don't write anything
under that.  then -2x minus +10x is really -2x-10x or -12x

            -2x² +  5x     
x + 2)-2x³ +  x² -  2x +  3
      -2x³ - 4x²
             5x² -  2x
             5x² + 10x
                  -12x  

Bring down the + 3

            -2x² +  5x     
x + 2)-2x³ +  x² -  2x +  3
      -2x³ - 4x²
             5x² -  2x
             5x² + 10x
                  -12x +  3
                  

-12x divided by x give -12.   Write that on the right at the top.

            -2x² +  5x - 12
x + 2)-2x³ +  x² -  2x +  3
      -2x³ - 4x²
             5x² -  2x
             5x² + 10x
                  -12x +  3
                   
-12 times +2 gives -24.  Write that under the +3

            -2x² +  5x - 12
x + 2)-2x³ +  x² -  2x +  3
      -2x³ - 4x²
             5x² -  2x
             5x² + 10x
                  -12x +  3
                       - 24
                          
-12 times x gives -12x

            -2x² +  5x - 12
x + 2)-2x³ +  x² -  2x +  3
      -2x³ - 4x²
             5x² -  2x
             5x² + 10x
                  -12x +  3
                  -12x - 24

Draw a line:

            -2x² +  5x - 12
x + 2)-2x³ +  x² -  2x +  3
      -2x³ - 4x²
             5x² -  2x
             5x² + 10x
                  -12x +  3
                  -12x - 24
                          

Subtract -12x - (-12x), that gives 0 so we don't write anything
under that.  then +3 minus -24 is really +3+24 or 27, so
the remainder is 27:

            -2x² +  5x - 12
x + 2)-2x³ +  x² -  2x +  3
      -2x³ - 4x²
             5x² -  2x
             5x² + 10x
                  -12x +  3
                  -12x - 24
                         27 

That's it. To write the answer we use 

-2x² + 5x - 12 + 

Edwin
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