SOLUTION: 7x^6-8x^4+7x^2+5 divided by x-2

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Question 712737: 7x^6-8x^4+7x^2+5 divided by x-2
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
While long division is always an option for division of polynomials, synthetic division can be used if the divisor is of the form: x - n. Since synthetic division is usually easier that is how I will do this. I hope you've been taught this method of division. (If not, ask your teacher to teach it!)
 2 |   7   0   -8   0   7   0   5   <== Note the 0's for the missing terms
----      14   28  40 160 334 668 
      ----------------------------
       7  14   20  80 167 334 673
The last number in the bottom row is the remainder. The rest of the bottom row is the quotient. The numbers "7 14 20 80 167 334" translate into:
7x%5E5%2B14x%5E4%2B20x%5E3%2B80x%5E2%2B167x%2B334. And the remainder, as usual, goes into the numerator of a fraction with the divisor as the denominator. So: