document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=896827>Question 896827</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that 1, 2, and 3 are roots of the degree five polynomial equation,<BR>\n" );
document.write( "x^5 -8x^4 + 15x^3 + 20x^2-76x + 48 = 0.<BR>\n" );
document.write( "The equation has two additional roots. What are they? (Hint: Avoid long division.)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #543772 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</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=543772\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your instructions suggest not using LONG DIVISION; but hopefully you are allowed to use SYNTHETIC DIVISION.\r<BR>\n" );
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document.write( "The possible roots to check for (using synthetic division) would be, other than the 1, 2, and 3; plus-and-minus of 4, 8, 12, 24 and maybe 48.  You are probably more interested in the negative roots, since there are a couple of sign changes in that degree-5 polynomial.  You might want to check -1, -2, or -3.\r<BR>\n" );
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document.write( "If you would perform the synthetic divisions for the given known roots, you would obtain a degree-two polynomial, easily analyzed for roots using general solution for quadratic equation.\r<BR>\n" );
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document.write( "I only described what could or should be done; not actually did it. </SPAN>\n" );
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