SOLUTION: (3x2 − 7x + 1) ÷ (3x − 1) please help with the above example pls show step by step on how you got the answer

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: (3x2 − 7x + 1) ÷ (3x − 1) please help with the above example pls show step by step on how you got the answer       Log On


   

Question 326560: (3x2 − 7x + 1) ÷ (3x − 1)
please help with the above example pls show step by step on how you got the answer
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
(3x2-7x+1)÷(3x-1)

Start with this:
                  `       
3x - 1)3x² - 7x + 1
      
Divide %283x%5E2%29%2F%283x%29 get x.
Write it above the -7x

              x   ` 
3x - 1)3x² - 7x + 1
     
Multiply the x by the 3x, getting 3x².
Write that under the 3x²:

              x   ` 
3x - 1)3x² - 7x + 1
       3x² 
   
Multiply the x by the -1, getting -x.
Write that under the -7x:
        
              x   ` 
3x - 1)3x² - 7x + 1
       3x² -  x
  
Draw a line:

              x   ` 
3x - 1)3x² - 7x + 1
       3x² -  x

Subtract                (3x² - 7x) - (3x² - x) 
                         3x² - 7x  -  3x² + x
                                 -6x
Write that under the line under -x
 

              x   ` 
3x - 1)3x² - 7x + 1
       3x² -  x
           - 6x 

Bring down the +1

              x   `  
3x - 1)3x² - 7x + 1
       3x² -  x
           - 6x + 1
            
Divide %28-6x%29%2F%283x%29 get -2.
Write that above the +1

              x - 2
3x - 1)3x² - 7x + 1
       3x² -  x
           - 6x + 1
            
Multiply the -2 by the 3x, getting -6x.
Write that under the -6x:                

              x - 2
3x - 1)3x² - 7x + 1
       3x² -  x
           - 6x + 1
            -6x 
                 
Multiply the -2 by the -1, getting +2.
Write that under the +1:


              x - 2
3x - 1)3x² - 7x + 1
       3x² -  x
           - 6x + 1
            -6x + 2
                 
Draw a line:

              x - 2
3x - 1)3x² - 7x + 1
       3x² -  x
           - 6x + 1
            -6x + 2

Subtract                (-6x + 1) - (-6x + 2) 
                         -6x + 1  +   6x - 2
                                 -1
Write that under the line under +2

              x - 2
3x - 1)3x² - 7x + 1
       3x² -  x
           - 6x + 1
            -6x + 2
                 -1


We have now finished the division.  Now
we make a fraction by placing the remainder
over the divisor getting %28-1%29%2F%283x-1%29

Now we add that to the quotient:

              x - 2 + %28-1%29%2F%283x-1%29
3x - 1)3x² - 7x + 1
       3x² -  x
           - 6x + 1
            -6x + 2
                 -1 


So the answer is at the top:

x%22%22-%22%222%22%22%2B%22%22%28-1%29%2F%283x-1%29

Or you can write it a tiny bit simpler as

x%22%22-%22%222%22%22-%22%221%2F%283x-1%29

Study those steps carefully.

Edwin