document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73374>Question 73374</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have learned how to completely factor polynomials such as: \r<BR>\n" );
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document.write( "x^2+7x-30<BR>\n" );
document.write( "(x+10)(x-3)\r<BR>\n" );
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document.write( "but I get lost when there are variables instead of number. I need to find all the positive values for \"k\" in this problem:\r<BR>\n" );
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document.write( "x^2+x-k </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52569 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=52569\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bx-k ALIGN=MIDDLE  ALT=\"x%5E2%2Bx-k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x%281%2F2%29%2B%281%2F2%29%5E2-%281%2F2%29%5E2-k ALIGN=MIDDLE  ALT=\"x%5E2%2B2x%281%2F2%29%2B%281%2F2%29%5E2-%281%2F2%29%5E2-k\"   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%2F2%29%5E2-%281%2F2%29%5E2-k ALIGN=MIDDLE  ALT=\"%28x%2B1%2F2%29%5E2-%281%2F2%29%5E2-k\"   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%2F2%29%5E2-1%2F4-k ALIGN=MIDDLE  ALT=\"%28x%2B1%2F2%29%5E2-1%2F4-k\"   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%2F2%29%5E2-%281%2F4%2Bk%29 ALIGN=MIDDLE  ALT=\"%28x%2B1%2F2%29%5E2-%281%2F4%2Bk%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This can be factorised if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%2B1%2F4 ALIGN=MIDDLE  ALT=\"k%2B1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a perfect square.<BR>\n" );
document.write( "Thus, those positive values of k which render <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%2B1%2F4 ALIGN=MIDDLE  ALT=\"k%2B1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > a perfect square are the reqd. values of k.<BR>\n" );
document.write( "So, k = 2, 6, 12, 20, 30, etc.\r<BR>\n" );
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document.write( "[Note that the difference between the consecutive terms form an A.P.: 4,6,8,10,.... ] </SPAN>\n" );
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