document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=964132>Question 964132</A>: <I><SPAN STYLE=\"word-break: break-all;\"> use the rational zeros theorem to find all zeros of the polynomial. Use the zeros to factor f over the real numbers.<BR>\n" );
document.write( "f(x)=x^3-5x^3-61x-55  show work </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #589079 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39623)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=589079\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Possible roots to check for would be -55, -11, -5, -1, 1, 5, 11, 55.<BR>\n" );
document.write( "There would be no more than eight synthetic divisions to perform in order to check for roots.  With so many to check, software to help would be preferable.  Otherwise, on paper, start with -5, -1, 1, and 5.  Simpler less advanced factoring might be enough after that.\r<BR>\n" );
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document.write( "First tried -5, myself.\r<BR>\n" );
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document.write( "__________-5____|______1_______-5_______-61_______-55<BR>\n" );
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document.write( "________________|______________-5________50________55<BR>\n" );
document.write( "________________|________________________________________<BR>\n" );
document.write( "_______________________1_________-10_______-11_______0\r<BR>\n" );
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document.write( "One root or zero is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5 ALIGN=MIDDLE  ALT=\"x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and the quadratic resulting is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-10x-11 ALIGN=MIDDLE  ALT=\"x%5E2-10x-11\"   DISABLED_style= \"max-width:90%; height:auto;\" >, easily factorable into  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-11%29%28x%2B1%29 ALIGN=MIDDLE  ALT=\"%28x-11%29%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x%2B5%29%28x-11%29%28x%2B1%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%2B5%29%28x-11%29%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The zeros are -5, 11, -1. </SPAN>\n" );
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