document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=201872>Question 201872</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find two negative values of \"k\" for which the given polynomial can be factored. (there may be many possible values)\r<BR>\n" );
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document.write( "Page 219, problem 39\r<BR>\n" );
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document.write( "r^2-2r+k\r<BR>\n" );
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document.write( "thank you very much for your help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #152118 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=152118\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In order for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2-2r%2Bk+ ALIGN=MIDDLE  ALT=\"r%5E2-2r%2Bk+\"   DISABLED_style= \"max-width:90%; height:auto;\" > to be factored, there must be two whole numbers that multiply to \"k\" AND add to -2. \r<BR>\n" );
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document.write( "So let's pick a random number. I'm going to pick 12. Now what number must I add to 12 to get -2? Well, we can set up the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2Bq=-2 ALIGN=MIDDLE  ALT=\"12%2Bq=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solve for \"q\" to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q=-2-12=-14 ALIGN=MIDDLE  ALT=\"q=-2-12=-14\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the numbers 12 and -14 add to -2. They multiply to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%29%28-14%29=-168 ALIGN=MIDDLE  ALT=\"%2812%29%28-14%29=-168\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So it turns out that the two numbers 12 and -14 both add to -2 (the middle coefficient) AND multiply to -168. So if we let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-168 ALIGN=MIDDLE  ALT=\"k=-168\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the polynomial <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2-2r-168 ALIGN=MIDDLE  ALT=\"r%5E2-2r-168\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored and it factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r%2B12%29%28r-14%29 ALIGN=MIDDLE  ALT=\"%28r%2B12%29%28r-14%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I'll let you find another value of \"k\". Simply use the logic used above to find another \"k\" value. </SPAN>\n" );
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