Question 16532
there is a procedure for short division called horner's method which can be used here. i shall show you 2 examples ..rest you can do in a similar manner..
 first write the given expression in decreasing order of powers listing missing terms also as zeros...
 For example   x^3-1 = 1*x^3+0*x^2+0*x-1..........(A)
  now check if we have the divisor in the form of x+a or x-a or not .we have here x-1 which is in the form x-a...then let x-1 =0 which gives us x=1...(B)
now do the division as follows
 write  1  0  0  -1......these are coefficients of powers of x obtained  above under (A)from the problem
  put 1 as divisor as obtained under (B) above
  do as follows
divisor...1]  1  0  0  -1......row 1
..................  0   1   1    1.......row 2
             --------------
..................  1   1   1    0 ......row 3
 explanation: row 1 has divisor on the left as 1 followed by a seperation bracket..then put coefficients of powers of x obtained  above under (A)from the problem in different columns
   row 2 ..start with a zero under the  coefficient  in row 1 in 1st.column..now add the row 1 and row 2 numbers in 1st. column  (which are there vertically one below the other )and put the sum under the same column in row 3...here 1+0=1..now multiply this number in row 3 with divisor and put it in row 2 in second column...now add numbers in row 1 and row 2 in column 2 put the sum in row 3 under same column no.2....repeat the procedure till the end 
row 3 represents the quotient and remainder...number in last column in row 3 is remainder here it is zero.the other numbers read from right to left give the coefficients of increasing powers of x ...that is the answer on division is 1x^2+1x+1..remainder =0
 to explain i am giving another example below...x^2-5x+6 devide by x-3
  put x-3 =0 so x=3 is the divisor...
   3]   1  -5  6
.....  0   3 -6
    --------------
.....  1  -2 0   answer is x-2 and remainder is 0