document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=922845>Question 922845</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I'm not sure where this problem is supposed to go so I just put it here.\r<BR>\n" );
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document.write( "Use synthetic division to show that x=7 is a root of the equation x^3-9x^2-1x+105=0.<BR>\n" );
document.write( "Then, use the result to factor the polynomial completely into the form (x+A)(x+B)(x+C).\r<BR>\n" );
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document.write( "thank you in advance! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #559759 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=559759\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The polynomial was made using binomial factors.  When they were multiplied and the result simplified and put into general form, the result became <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3-9x%5E2-1x%2B105 ALIGN=MIDDLE  ALT=\"x%5E3-9x%5E2-1x%2B105\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now, you want to test for different possible binomial factors to see which ones are pefect divisors of the polynomial, meaning the remainder is zero.  You are guided with the instruction to first test the root x=7, which corresponds to the binomial factor of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-7 ALIGN=MIDDLE  ALT=\"x-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "_______7_____|______1______-9______-1________105<BR>\n" );
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document.write( "_____________|_____________7_______-14_______-105<BR>\n" );
document.write( "_____________|_______________________________________<BR>\n" );
document.write( "____________________1_______-2_____-15________0\r<BR>\n" );
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document.write( "The remainder is 0; x=7 is a root of the given polynomial.<BR>\n" );
document.write( "The resulting quotient means that the quotient is really <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x-15 ALIGN=MIDDLE  ALT=\"x%5E2-2x-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which you will either factor if possible and you can find the combination or use general solution for quadratic formula.\r<BR>\n" );
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document.write( "Simple factoring trials should be enough <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%28x-5%29=0=x%5E2-2x-15 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%28x-5%29=0=x%5E2-2x-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The factorization for the given equation is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28x-7%29%28x-5%29%28x%2B3%29=0%29 ALIGN=MIDDLE  ALT=\"highlight%28%28x-7%29%28x-5%29%28x%2B3%29=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or any arrangement equivalent according to commutative property for multiplication. </SPAN>\n" );
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