document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=816155>Question 816155</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How to factor 2x^3-x^2-10x+5 by grouping </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #491738 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=491738\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E3-x%5E2-10x%2B5 ALIGN=MIDDLE  ALT=\"2x%5E3-x%5E2-10x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I find that factoring by grouping is easier if you<ul><li>Change any subtractions into equivalent additions.</li><li>When factoring out the greatest common factor (GCF) from each group, consider factoring out the negative of the GCF from just one of the groups.</li></ul>Let's see this on your expression. First, change the subtractions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E3%2B%28-x%5E2%29%2B%28-10x%29%2B5 ALIGN=MIDDLE  ALT=\"2x%5E3%2B%28-x%5E2%29%2B%28-10x%29%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we group:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%5E3%2B%28-x%5E2%29%29%2B%28%28-10x%29%2B5%29 ALIGN=MIDDLE  ALT=\"%282x%5E3%2B%28-x%5E2%29%29%2B%28%28-10x%29%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Next we factor out the GCF from each group. The GCF of the first group is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The GCF of the second group is 5. Factoring these out we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%7B2x%2B%28-1%29%29%2B5%28%28-2x%29%2B1%29 ALIGN=MIDDLE  ALT=\"x%5E2%7B2x%2B%28-1%29%29%2B5%28%28-2x%29%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "As we can see the \"non-GCF\" factors, (2x+(-1)) and (-2x+1) are not the same. So it appears that factoring by grouping is not working for us. But these two factors are exact opposites of each other. This is when factoring our the negative of the GCF can be very helpful. Instead of factoring 5 out of the second group of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E3%2B%28-x%5E2%29%29%2B%28%28-10x%29%2B5%29 ALIGN=MIDDLE  ALT=\"2x%5E3%2B%28-x%5E2%29%29%2B%28%28-10x%29%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we will factor out -5:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%282x%2B%28-1%29%29%2B%28-5%29%282x%2B%28-1%29%29 ALIGN=MIDDLE  ALT=\"x%5E2%282x%2B%28-1%29%29%2B%28-5%29%282x%2B%28-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now the \"non-GCF\" factors are the same and we can proceed. Next we factor out the GCF of the two groups, (2x+(-1)):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B%28-1%29%29%28x%5E2%2B%28-5%29%29 ALIGN=MIDDLE  ALT=\"%282x%2B%28-1%29%29%28x%5E2%2B%28-5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since neither of these factors will factor further, we are finished factoring. At this point additions of negatives may be changed back to subtractions if you prefer. So the answer is either<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B%28-1%29%29%28x%5E2%2B%28-5%29%29 ALIGN=MIDDLE  ALT=\"%282x%2B%28-1%29%29%28x%5E2%2B%28-5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-1%29%28x%5E2-5%29 ALIGN=MIDDLE  ALT=\"%282x-1%29%28x%5E2-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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