SOLUTION: I am not understanding the long division I have seen examples but not understanding how and where they are getting what to divide 7. Divide using synthetic division (4x4 + 6x

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Question 1040602: I am not understanding the long division I have seen examples but not understanding how and where they are getting what to divide
7. Divide using synthetic division
(4x4 + 6x3 + 3x – 1)  (2x2 + 1)

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Polynomial long division works the same way as regular long division of decimal numbers. THE SAME WAY. Abbreviations are not done so you can see the entire part of each step.

Your dividend is 4x%5E4%2B6x%5E3%2B0x%5E2%2B3x-1, because you must account for all degrees of x up to the degree of the dividend. Your divisor is 2x%5E2%2B1 and you might want but not need to use it as 2x%5E2%2B0x%2B1.

You will expect that divisor is less than dividend, and ask yourself what is the quotient of the leading terms. This will be the first partial quotient to start the process. I will not explain the rest but will show just the start...

4x%5E4%2F2x%5E2=2x%5E2; indicate this partial quotient.  Multiply this by the divisor, and put result in proper positions.
 

               2x^2
          _____________________________________________
2x^2+1    |    4x^4    6x^3    0x^2     3x      -1
          |
          |   4x^4      0x^2   2x^2
          |


Do the necessary subtraction.

               2x^2
          __________________________________________________
2x^2+1    |    4x^4    6x^3    0x^2     3x      -1
          |
          |   4x^4      0x^2   2x^2
          |__________________________
               0       6x^2   -2x^2


Bring down the next term, or terms, and continue.  You would then be asking yourself, what is  %286x%5E2%29%2F%282x%5E2%29.