document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=20643>Question 20643</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the roots of this polynomial equation:<BR>\n" );
document.write( "x³ - 5x² + 2x + 8 = 0\r<BR>\n" );
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document.write( "how do I do this i am so confused please help me. I need to know the steps to finding the answer..<BR>\n" );
document.write( "Becca </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #9933 by </B><A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><B>AnlytcPhil(1806)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><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=AnlytcPhil><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=9933\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face = \"courier new\" size = 3>find the roots of each polynomial equation:<BR>\n" );
document.write( "x(cubed)-5x(squared)+2x+8=0<BR>\n" );
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document.write( "x³ - 5x² + 2x + 8 = 0<BR>\n" );
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document.write( "Since the coefficient of x³ is 1, if it has any real rational roots,<BR>\n" );
document.write( "they have to be a divisor of the absolute value of the constant term in<BR>\n" );
document.write( "absolute value. So we can try +1, -1, +2, -2, +4, -4, +8, or -8<BR>\n" );
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document.write( "Try the easiest one first. Substitute x=1, you get <BR>\n" );
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document.write( "(1)³ - 5(1)² + 2(1) + 8 = 0<BR>\n" );
document.write( "` ` ` ` `1 - 5 + 2 + 8 = 0<BR>\n" );
document.write( "` ` ` ` ` ` ` ` ` ` `6 = 0<BR>\n" );
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document.write( "Nope, 1 is not a root.  So try substituting x=-1, you get<BR>\n" );
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document.write( "(-1)³ - 5(-1)² + 2(-1) + 8 = 0<BR>\n" );
document.write( "` ` ` ` -1 - 5 - 2 + 8 = 0<BR>\n" );
document.write( "` ` ` ` ` ` ` ` ` ` `0 = 0<BR>\n" );
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document.write( "Yes that's a solution, so if x = -1 is a root, that means<BR>\n" );
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document.write( "x + 1 is a factor, because if you set that = 0 you'll get x = -1.<BR>\n" );
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document.write( "So divide by x+1, you use synthetic division, using -1 in the far left:<BR>\n" );
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document.write( "-1 | 1 -5  2 `8<BR>\n" );
document.write( "` `|___-1_6_-8_ <BR>\n" );
document.write( "` ` `1 -6  8 `0<BR>\n" );
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document.write( "The numbers on the bottom mean x²-6x+8 with the last number 0 <BR>\n" );
document.write( "being the remainder, which is how you know x+1 was a factor of <BR>\n" );
document.write( "the polynomial. So you now have the polynomial equation factored <BR>\n" );
document.write( "as<BR>\n" );
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document.write( "(x+1)(x²-6x+8) = 0<BR>\n" );
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document.write( "You can now factor the trinomial in the second parentheses as <BR>\n" );
document.write( "(x-2)(x-4) and get <BR>\n" );
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document.write( "(x+1)(x-2)(x-4)=0<BR>\n" );
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document.write( "Set each of those three parenthetical expressions = 0, and get -1, 2, <BR>\n" );
document.write( "and 4.<BR>\n" );
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document.write( "Edwin<BR>\n" );
document.write( "AnlytcPhil@aol.com\r<BR>\n" );
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document.write( "   <BR>\n" );
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