document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204305>Question 1204305</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine whether the binomial (3x  -  2) is a factor of the polynomial <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E3-14x%5E2%2B26x-12 ALIGN=MIDDLE  ALT=\"3x%5E3-14x%5E2%2B26x-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<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 #840470 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52786)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=840470\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Determine whether the binomial (3x-2) is a factor of the polynomial <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E3-14x%5E2%2B26x-12 ALIGN=MIDDLE  ALT=\"3x%5E3-14x%5E2%2B26x-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Alternatively to other methods, you can factor the polynomial explicitly, <BR>\n" );
document.write( "using the grouping and re-grouping method and applying it step by step.\r<BR>\n" );
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document.write( "This is made easier by the fact that the basic binomial 3x-2 is just given to work with it.\r<BR>\n" );
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document.write( "3x^3 - 14x^2 + 26x - 12 = group and re-group the terms step by step = (3x^2 - 2x^2) - 12x^2 + 26x - 12 = \r<BR>\n" );
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document.write( "= x^2*(3x-2) - (12x^2 -26x) - 12 = x^2*(3x-2) - (12x^2 - 8x) - 8x + 26x - 12 = x^2*(3x-2) - 4x(3x-2) + (18x-12) = \r<BR>\n" );
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document.write( "= x^2*(3x-2) - 4x(3x-2) + 6(3x-2) = take off the common factor (3x-2) = (3x-2)*(x^2 - 4x + 6).\r<BR>\n" );
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document.write( "The last formula shows explicitly that (3x-2) is the factor.<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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