3x^4-5x^2+10/x-7

Question

 divide the polynomial by synthetic division

Answer 1

Here is how you divide it with synthetic division:

 

First, list out all the terms 

 

3x^4,   5x^2,   10       ...........   x-7

 

Add in the missing variables

 

3x^4, 0x^3, 5x^2, 0x, 10 ..... x-7

 

Then take away the variables (no need for those pesky letters in this equation!)

   3,    0,    5,    0,     10   .......  7 (take the opposite sign of the divisor)

 

Then, set up the division problem and automatically bring the first digit down 

 

7| 3    0    -5    0    10

   ________________

    3

 

Multiply that number to the 7, put that in the next space and add

 

7| 3    0    -5    0    10
         21 

  _________________
    3   21

 

Continue doing the same thing down the line

 

7| 3    0    -5    0    10

         21   147  

  _________________
   3    21   142

 

7| 3    0    -5    0    10
         21   147 994
    ________________

    3   21   142 994

 

7| 3    0    -5    0    10
         21  147 994  6958
  _________________
    3   21  142 994  6968

 

Then, here comes the fun part...add on the variables to make it look like an equation again! Be sure to put the last number over the divisor (since that's the remainder)

 

...and VOILA!

Answer:   3x^3+21x^2+142x+994+(6968/(x-7))

 

 

Answer 2

 

7|     3       0       -5            0         10

                21     147        994             6958

        3      21      142        994  

 

 

6968

 

Got the same answer as Robert J.   Nice job Robert.

Answer 3

7|  3    0     -5      0       10

         21   147  994   6958

     3  21   142  994   6968

3x³+21x²+142x+994 with remainder 6968

The check for the remainder

3×7⁴-5×7²+10=6968

 

Answer 4

7 | 3 0 ..-5....0.... 10

.......21 147 994. 6958

-----------------

....3 21 142 994|6968

 

Answer:

(3x^4-5x^2+10)/(x-7) = 3x^3+21x^2+142x+994 + 6968/(x-7)