document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=661407>Question 661407</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (-a2square+3a-2)(a2square+3a-2)\r<BR>\n" );
document.write( "\n" );
document.write( "How do I solve this problem? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #411605 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=411605\">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=%28-a%5E2%2B3a-2%29%28a%5E2%2B3a-2%29+ ALIGN=MIDDLE  ALT=\"%28-a%5E2%2B3a-2%29%28a%5E2%2B3a-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...set it equal to zero and solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-a%5E2%2B3a-2%29%28a%5E2%2B3a-2%29=0+ ALIGN=MIDDLE  ALT=\"%28-a%5E2%2B3a-2%29%28a%5E2%2B3a-2%29=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >...here you have the product of two polynomial, and that product will e equal to zero if either one or both of them is equal to zero\r<BR>\n" );
document.write( "\n" );
document.write( "so, take this factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-a%5E2%2B3a-2%29=0+ ALIGN=MIDDLE  ALT=\"%28-a%5E2%2B3a-2%29=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > that makes it equal to zero\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-a%5E2%2B3a-2%29=0+ ALIGN=MIDDLE  ALT=\"%28-a%5E2%2B3a-2%29=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >...use quadratic formula..(don't be confused with unknown variable labeled with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, same as a coefficient <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >)  \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A%28-1%29%2A%28-2%29+%29%29%2F%282%2A%28-1%29%29+ ALIGN=MIDDLE  ALT=\"a+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A%28-1%29%2A%28-2%29+%29%29%2F%282%2A%28-1%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%28-3+%2B-+sqrt%28+9-8+%29%29%2F-2+ ALIGN=MIDDLE  ALT=\"a+=+%28-3+%2B-+sqrt%28+9-8+%29%29%2F-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%28-3+%2B-+sqrt%28+1+%29%29%2F-2+ ALIGN=MIDDLE  ALT=\"a+=+%28-3+%2B-+sqrt%28+1+%29%29%2F-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%28-3+%2B-+1%29%2F-2+ ALIGN=MIDDLE  ALT=\"a+=+%28-3+%2B-+1%29%2F-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "solutions:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%28-3+%2B+1%29%2F-2+ ALIGN=MIDDLE  ALT=\"a+=+%28-3+%2B+1%29%2F-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+-2%2F-2+ ALIGN=MIDDLE  ALT=\"a+=+-2%2F-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a+=+1%29+ ALIGN=MIDDLE  ALT=\"highlight%28a+=+1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%28-3+-1%29%2F-2+ ALIGN=MIDDLE  ALT=\"a+=+%28-3+-1%29%2F-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+-4%2F-2+ ALIGN=MIDDLE  ALT=\"a+=+-4%2F-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a+=+2%29+ ALIGN=MIDDLE  ALT=\"highlight%28a+=+2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "now, do the same with second factor in given product\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2B3a-2=0+ ALIGN=MIDDLE  ALT=\"a%5E2%2B3a-2=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A1%2A%28-2%29+%29%29%2F%282%2A1%29%29+ ALIGN=MIDDLE  ALT=\"a+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A1%2A%28-2%29+%29%29%2F%282%2A1%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%28-3+%2B-+sqrt%289%2B8+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"a+=+%28-3+%2B-+sqrt%289%2B8+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%28-3+%2B-+sqrt%2817+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"a+=+%28-3+%2B-+sqrt%2817+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%28-3+%2B-+4.12%29%29%2F2+ ALIGN=MIDDLE  ALT=\"a+=+%28-3+%2B-+4.12%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solutions:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%28-3+%2B4.12%29%2F2+ ALIGN=MIDDLE  ALT=\"a+=+%28-3+%2B4.12%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+1.12%2F2+ ALIGN=MIDDLE  ALT=\"a+=+1.12%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a+=+0.56%29+ ALIGN=MIDDLE  ALT=\"highlight%28a+=+0.56%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%28-3+-4.12%29%2F2+ ALIGN=MIDDLE  ALT=\"a+=+%28-3+-4.12%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+-7.12%2F2+ ALIGN=MIDDLE  ALT=\"a+=+-7.12%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a+=+-3.56%29+ ALIGN=MIDDLE  ALT=\"highlight%28a+=+-3.56%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "so, there are four solutions because, if you multiply given polynomials you will get polynomial of fourth degree <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a%5E4%2B9a%5E2-12a%2B4 ALIGN=MIDDLE  ALT=\"-a%5E4%2B9a%5E2-12a%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28600%2C+600%2C+-5%2C+5%2C+-5%2C+55%2C+-x%5E4%2B9x%5E2-12x%2B4%29+ ALIGN=MIDDLE  ALT=\"+graph%28600%2C+600%2C+-5%2C+5%2C+-5%2C+55%2C+-x%5E4%2B9x%5E2-12x%2B4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );