SOLUTION: I am having a real problem with long division. This is the problem I have: (2u^3-13u^2-8u+7) divided by (u-7)

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Question 334031: I am having a real problem with long division. This is the problem I have:
(2u^3-13u^2-8u+7) divided by (u-7)

Found 2 solutions by mananth, Edwin McCravy:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
........2u^2 +u -1
-----------------------
(u-7) |(2u^3-13u^2-8u+7)
.......(-)2u^3 -14u^2
-----------
........u^2-8u
.....(-)u^2-7u
---------
.........-u+7
......(-)-u+7
----------------


Answer by Edwin McCravy(20059)   (Show Source): You can put this solution on YOUR website!
(2u^3-13u^2-8u+7) divided by (u-7)

Start with this:            
     ____________________ 
u - 7)2u³ - 13u² - 8u + 7

u on the far left divided into 2u³ gives 2u², so put 2u² on top of the line

 
             2u²        ` 
u - 7)2u³ - 13u² - 8u + 7
 
Multiply the 2u² by the u, getting 2u³, write that down under the
other 2u²:
   
             2u²        `
u - 7)2u³ - 13u² - 8u + 7
      2u³ 

Multiply the 2u² by the -7, getting -14u², write that down under the
-13u²:


             2u²        `
u - 7)2u³ - 13u² - 8u + 7
      2u³ - 14u²

Draw a line at the bottom:

             2u²        `
u - 7)2u³ - 13u² - 8u + 7
      2u³ - 14u²


Now we subtract, by thinking of changing the sign of
the 2u³ to -2u³ and adding, and so it cancels out.
We also subtract the other terms, by thinking of changing 
the sign of the -14u² to +14u² and adding, and we get +1u² 
or just u². We write that below the line:

             2u²        `
u - 7)2u³ - 13u² - 8u + 7
      2u³ - 14u²
              u² 

Now we bring down the -8u:

             2u²        `
u - 7)2u³ - 13u² - 8u + 7
      2u³ - 14u²
              u² - 8u

u on the far left divided into u² at the bottom, gives + u,
so put + u on top of the top line

             2u² +  u   `
u - 7)2u³ - 13u² - 8u + 7
      2u³ - 14u²
              u² - 8u

Multiply the u on top by the u at the far left, getting u², 
write that down under the other u²:

             2u² +  u   `
u - 7)2u³ - 13u² - 8u + 7
      2u³ - 14u²
              u² - 8u
              u²

Multiply the u on top by the - 7, getting -7u, write that 
down under the 8u:

             2u² +  u   `
u - 7)2u³ - 13u² - 8u + 7
      2u³ - 14u²
              u² - 8u
              u² - 7u

Draw a line at the bottom:

             2u² +  u   `
u - 7)2u³ - 13u² - 8u + 7
      2u³ - 14u²
              u² - 8u
              u² - 7u

Now we subtract, by thinking of changing the sign of
the lower u² to -u³ and adding, and so it cancels out.
We also subtract the other terms, by thinking of changing 
the sign of the - 8u to +8u and adding, and we get -u.
We write that below the line:

             2u² +  u   `
u - 7)2u³ - 13u² - 8u + 7
      2u³ - 14u²
              u² - 8u
              u² - 7u
                   -u 

Now we bring down the + 7

             2u² +  u   `
u - 7)2u³ - 13u² - 8u + 7
      2u³ - 14u²
              u² - 8u
              u² - 7u
                   -u + 7

u on the far left divided into -u at the bottom, gives - 1,
so put - 1 on top of the top line

             2u² +  u - 1
u - 7)2u³ - 13u² - 8u + 7
      2u³ - 14u²
              u² - 8u
              u² - 7u
                   -u + 7
                   
Multiply the - 1 on top by the u at the far left, getting -u,
write that down under the other -u:

             2u² +  u - 1
u - 7)2u³ - 13u² - 8u + 7
      2u³ - 14u²
              u² - 8u
              u² - 7u
                   -u + 7
                   -u 

Multiply the - 1 on top by the - 7, getting + 7, write that 
down under the other + 7


             2u² +  u - 1
u - 7)2u³ - 13u² - 8u + 7
      2u³ - 14u²
              u² - 8u
              u² - 7u
                   -u + 7
                   -u + 7

Draw a line underneath:

             2u² +  u - 1
u - 7)2u³ - 13u² - 8u + 7
      2u³ - 14u²
              u² - 8u
              u² - 7u
                   -u + 7
                   -u + 7



Now we subtract, by thinking of changing the sign of
the lower -u to +u and adding, and so it cancels out.
We also subtract the other terms, by thinking of changing 
the sign of the + 7 to - 7 and adding, and we get 0.
We write that below the line:

             2u² +  u - 1
u - 7)2u³ - 13u² - 8u + 7
      2u³ - 14u²
              u² - 8u
              u² - 7u
                   -u + 7
                   -u + 7
                        0

The remainder is 0.  So we are done and the quotient is

u² + u - 1

When the remainder isn't 0 we have to add a fraction 
expression to the quotient whose numerator is the remainder and whose
denominator is the divisor.

Edwin

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