Question 712737
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!)
<pre>
 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
</pre>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^5+14x^4+20x^3+80x^2+167x+334}}}. And the remainder, as usual, goes into the numerator of a fraction with the divisor as the denominator. So:
{{{(7x^6-8x^4+7x^2+5)/(x-2) = 7x^5+14x^4+20x^3+80x^2+167x+334 + 672/(x-2)}}}