document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=885807>Question 885807</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Multiply each of the polynomial by x+1 with solution:<BR>\n" );
document.write( "a. x-1<BR>\n" );
document.write( "b. x^2-x+1<BR>\n" );
document.write( "c. x^3-x^2+x-1<BR>\n" );
document.write( "d. x^4-x^3+x^2-x+1<BR>\n" );
document.write( "2. Look for the pattern in Question 1 and use it to multiply:<BR>\n" );
document.write( "(x+1) (x^8-x^7+x^6-x^5+x^4-x^3+x^2-x+1)<BR>\n" );
document.write( "3. Predict what you think will be the product of (x+1) and (x^100-x^98+x^97...x^2-x+1) when simplified, can you explain why you're must be correct?<BR>\n" );
document.write( "All should have a solution. Please help. :)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #535747 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=535747\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%2A%28x-1%29=x%2A%28x-1%29%2B1%2A%28x-1%29=x%5E2-x%2Bx-1=x%5E2-1 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%2A%28x-1%29=x%2A%28x-1%29%2B1%2A%28x-1%29=x%5E2-x%2Bx-1=x%5E2-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%2A%28x%5E2-x%2B1%29=x%2A%28x%5E2-x%2B1%29%2B1%2A%28x%5E2-x%2B1%29=x%5E3-x%5E2%2Bx%2Bx%5E2-x%2B1=x%5E3%2B1 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%2A%28x%5E3-x%5E2%2Bx-1%29=x%2A%28x%5E3-x%5E2%2Bx-1%29%2B1%2A%28x%5E3-x%5E2%2Bx-1%29=x%5E4-x%5E3%2Bx%5E2-x%2Bx%5E3-x%5E2%2Bx-1=x%5E4-1 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%2A%28x%5E4-x%5E3%2Bx%5E2-x%2B1%29=x%2A%28x%5E4-x%5E3%2Bx%5E2-x%2B1%29%2B1%2A%28x%5E4-x%5E3%2Bx%5E2-x%2B1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >=?<BR>\n" );
document.write( "Those two products would be too long to write in one line, so I will add them up vertically:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28150%2C100%2C0%2C4.5%2C-3%2C0%2C%0D%0Alocate%280%2C0%2Cx%5E5-x%5E4%2Bx%5E3-x%5E2%2Bx%29%2C%0D%0Alocate%280.55%2C-0.9%2C%22%2B%22%29%2C%0D%0Alocate%280.85%2C-0.7%2Cx%5E4-x%5E3%2Bx%5E2-x%2B1%29%2C%0D%0Aline%280%2C-1.6%2C4.5%2C-1.6%29%2C%0D%0Alocate%280%2C-1.7%2Cx%5E5%29%2Clocate%283.6%2C-2%2C%22%2B%22%29%2Clocate%284%2C-2%2C1%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%2A%28x%5E4-x%5E3%2Bx%5E2-x%2B1%29=X%5E6%2B1 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%2A%28x%5E4-x%5E3%2Bx%5E2-x%2B1%29=X%5E6%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "2) In all the products above <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29 ALIGN=MIDDLE  ALT=\"%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is one factor,<BR>\n" );
document.write( "and the other factor is a polynomial with sign that alternate,<BR>\n" );
document.write( "so all the middle products cancel out.<BR>\n" );
document.write( "You are left with just the product of the first terms plus the product of the last terms.<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%2A%28x%5E8-x%5E7%2Bx%5E6-x%5E5%2Bx%5E4-x%5E3%2Bx%5E2-x%2B1%29=x%5E9%2B1 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%2A%28x%5E8-x%5E7%2Bx%5E6-x%5E5%2Bx%5E4-x%5E3%2Bx%5E2-x%2B1%29=x%5E9%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "All the other products cancel out and you are left with the product of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29 ALIGN=MIDDLE  ALT=\"%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > times the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E8 ALIGN=MIDDLE  ALT=\"x%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "plus the product of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%2B1%22 ALIGN=MIDDLE  ALT=\"%22%2B1%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%2B1%22 ALIGN=MIDDLE  ALT=\"%22%2B1%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > at the end of both factors.<BR>\n" );
document.write( " <BR>\n" );
document.write( "3) I believe what you meant to write was<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%2A%28x%5E100-x%5E99%2Bx%5E98-x%5E97%2B+%22...%22+%2Bx%5E2-x%2B1%29 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%2A%28x%5E100-x%5E99%2Bx%5E98-x%5E97%2B+%22...%22+%2Bx%5E2-x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , because if the signs alternate,<BR>\n" );
document.write( "all the terms with even exponents will follow a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%2B%22 ALIGN=MIDDLE  ALT=\"%22%2B%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > sign.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%2A%28x%5E100-x%5E99%2Bx%5E98-x%5E97%2B+%22...%22+%2Bx%5E2-x%2B1%29=x%5E101%2B1 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%2A%28x%5E100-x%5E99%2Bx%5E98-x%5E97%2B+%22...%22+%2Bx%5E2-x%2B1%29=x%5E101%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );