SOLUTION: I have the following: {{{(2x^2-18x+8)/(2x-4)}}}. The instructions are to divide. I believe the answer to be x-7 with a remainder of 10/x-2. However, I am not sure how to check i

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I have the following: {{{(2x^2-18x+8)/(2x-4)}}}. The instructions are to divide. I believe the answer to be x-7 with a remainder of 10/x-2. However, I am not sure how to check i      Log On


   

Question 81556: I have the following: %282x%5E2-18x%2B8%29%2F%282x-4%29. The instructions are to divide. I believe the answer to be x-7 with a remainder of 10/x-2. However, I am not sure how to check if this answer is correct. Would you please help me solve?
Thank you.
Found 2 solutions by doctor_who, Edwin McCravy:
Answer by doctor_who(15) About Me  (Show Source):
You can put this solution on YOUR website!
It's a shame it's 18x and not 8x otherwise it would divide nice and easily. However, if it really is 18x then your answer looks on the right lines to me.
Here's how I did it.
___
Starting out, we can divide both the top and the bottom by 2 to get :
(x^2 - 9x + 4)/(x-2)
Now, the top half is almost (x-2)(x-7), (it looks like you spotted this) since (x-2)(x-7) = 2x^2 - 9x + 14.
So we can re-write as
((x-2)(x-7)-10)/(x-2)
Which leads to: (x-7) - 10/(x-2)

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

Solution by Edwin McCravy:

I don't think Dr. Who used the method you were taught, 
so I thought I'd do it the way I think you were taught.
Also, he didn't tell you how to check it.


I have the following: %282x%5E2-18x%2B8%29%2F%282x-4%29.  The instructions are to divide.  
I believe the answer to be x-7 with a remainder of 10/x-2.  However, I am
not sure how to check if this answer is correct. Would you please help me 
solve?

Thank you. 


So you started with  

 2x² - 18x + 8
---------------  
    2x - 4

and got

          10
x - 7 + -------
         x - 2 

The best way to check to see if that is right
is to:
 
1. substitute 0 for x in the original.
2. substitute 0 for x in the final answer.
3. If you don't get the same thing then you
   have made an error.
4. If you got the same thing in steps 1 and 2,
   then you still may have made an error, so:
5. Substitute 1 for x in the original. 
6. Substitute 1 for x in the final.
7. If you get the same thing then you are 99%
   certain you are correct. If not, you have made 
   an error.
(Note: if the divisor is 0 when you substitute 1 in
step 5, then substitute 2 instead of 1 in 6 and 7.

Let's check yours:

1. substitute 0 for x in the original.

 2x² - 18x + 8
---------------  
    2x - 4

 2(0)² - 18(0) + 8       8 
------------------- =  ---- = -2 
    2(0) - 4            -4

2. substitute 0 for x in your final answer.

          10
x - 7 + -------
         x - 2 

          10
0 - 7 + ------- = -7 - 5 = -12
         0 - 2 

Oh oh!  Those are not the same.  So we don't
need to substitute 1.  You made an error.

Let's do it again:

               x -  7 
2x - 4)2x² - 18x +  8
       2x² -  4x
            -14x +  8
            -14x + 28
                  -20

Write the -20 over the divisor and add to the
quotient.  The answer, before simplifying, is

          -20
x - 7 + ---------
         2x - 4 

On the bottom you can factor out a 2

           -20
x - 7 + ----------
         2(x - 2) 

Now you can cancel the 2 on the bottom into
the -20 on top and get -10 

           -10 
           -20
x - 7 + ----------
         2(x - 2) 
         1

          -10
x - 7 + --------
         x - 2

So it looks like you made an error in the sign of
the remainder.  You can now bring the negative sign
out front of the fraction and have:

           10
x - 7 - --------
         x - 2

as our new final answer.

Now let's check it:

1. substitute 0 for x in the original.

 2x² - 18x + 8
---------------  
    2x - 4

 2(0)² - 18(0) + 8       8 
------------------- =  ---- = -2 
    2(0) - 4            -4

2. substitute 0 for x in our new final answer.

          10
x - 7 - -------
         x - 2 

          10
0 - 7 - ------- = -7 - (-5) = -7 + 5 = -2
         0 - 2 


3. We got the same thing.
4. Since we got the same thing in steps 1 and 2,
   then:
5. Substitute 1 for x in the original. 

 2x² - 18x + 8
---------------  
    2x - 4

 2(1)² - 18(1) + 8      -8 
------------------- =  ---- = +4 
    2(1) - 4            -2


6. Substitute 1 for x in our new final answer:

          10
x - 7 - -------
         x - 2 

          10            10
1 - 7 - ------- = -6 - ---- = -6 - (-10) = -6 + 10 = +4  
         1 - 2          -1

7. We get the same thing so we are now 99% sure that
   this is correct.  This is not an absolutely perfect
   check, but the first three steps (substituting 0)
   will nearly always catch an error.
   
Edwin