document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=16532>Question 16532</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Divide x^3 - 1 by x - 1, x^4 - 1 by  x - 1, and x^5 - 1 by x - 1.  What is the quotient when x^9 - 1 is divided by x - 1? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #8067 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=8067\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 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..<BR>\n" );
document.write( " first write the given expression in decreasing order of powers listing missing terms also as zeros...<BR>\n" );
document.write( " For example   x^3-1 = 1*x^3+0*x^2+0*x-1..........(A)<BR>\n" );
document.write( "  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)<BR>\n" );
document.write( "now do the division as follows<BR>\n" );
document.write( " write  1  0  0  -1......these are coefficients of powers of x obtained  above under (A)from the problem<BR>\n" );
document.write( "  put 1 as divisor as obtained under (B) above<BR>\n" );
document.write( "  do as follows<BR>\n" );
document.write( "divisor...1]  1  0  0  -1......row 1<BR>\n" );
document.write( "..................  0   1   1    1.......row 2<BR>\n" );
document.write( "             --------------<BR>\n" );
document.write( "..................  1   1   1    0 ......row 3<BR>\n" );
document.write( " 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<BR>\n" );
document.write( "   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 <BR>\n" );
document.write( "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<BR>\n" );
document.write( " to explain i am giving another example below...x^2-5x+6 devide by x-3<BR>\n" );
document.write( "  put x-3 =0 so x=3 is the divisor...<BR>\n" );
document.write( "   3]   1  -5  6<BR>\n" );
document.write( ".....  0   3 -6<BR>\n" );
document.write( "    --------------<BR>\n" );
document.write( ".....  1  -2 0   answer is x-2 and remainder is 0\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
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