document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=297228>Question 297228</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Factor completely 8w^7+6w^6-20w^5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #214089 by </B><A HREF=/tutors/aboutme.mpl?userid=JBarnum><B>JBarnum(2146)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=JBarnum><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=JBarnum><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=214089\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2 is the GCF of 8,6,and 20<BR>\n" );
document.write( "w^5 is the GCF of w^7,w^6,w^5<BR>\n" );
document.write( "so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%5E5%284w%5E2%2B3w-10%29 ALIGN=MIDDLE  ALT=\"2w%5E5%284w%5E2%2B3w-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > do quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%5E5%284%28w-1.25%29%28w%2B2%29%29 ALIGN=MIDDLE  ALT=\"2w%5E5%284%28w-1.25%29%28w%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8w%5E5%28w-1.25%29%28w%2B2%29%29 ALIGN=MIDDLE  ALT=\"8w%5E5%28w-1.25%29%28w%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > completely factored<BR>\n" );
document.write( "__________________<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=aw%5E2%2Bbw%2Bc=0 ALIGN=MIDDLE  ALT=\"aw%5E2%2Bbw%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4w%5E2%2B3w%2B-10+=+0 ALIGN=MIDDLE  ALT=\"4w%5E2%2B3w%2B-10+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"w%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%283%29%5E2-4%2A4%2A-10=169 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%283%29%5E2-4%2A4%2A-10=169\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=169 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-3%2B-sqrt%28+169+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-3%2B-sqrt%28+169+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5B1%5D+=+%28-%283%29%2Bsqrt%28+169+%29%29%2F2%5C4+=+1.25 ALIGN=MIDDLE  ALT=\"w%5B1%5D+=+%28-%283%29%2Bsqrt%28+169+%29%29%2F2%5C4+=+1.25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5B2%5D+=+%28-%283%29-sqrt%28+169+%29%29%2F2%5C4+=+-2 ALIGN=MIDDLE  ALT=\"w%5B2%5D+=+%28-%283%29-sqrt%28+169+%29%29%2F2%5C4+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4w%5E2%2B3w%2B-10 ALIGN=MIDDLE  ALT=\"4w%5E2%2B3w%2B-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4w%5E2%2B3w%2B-10+=+4%28w-1.25%29%2A%28w--2%29 ALIGN=MIDDLE  ALT=\"4w%5E2%2B3w%2B-10+=+4%28w-1.25%29%2A%28w--2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 1.25, -2.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B3%2Ax%2B-10+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B3%2Ax%2B-10+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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