document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=157688>Question 157688</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 7.08x^6 + 4.15x^3 - 9.6 = 0\r<BR>\n" );
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document.write( "Is it possible to factor this equation? I would really appreciate the help.\r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #116492 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=116492\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 7.08x^6 + 4.15x^3 - 9.6 = 0 <BR>\n" );
document.write( "Is it possible to factor this equation? I would really appreciate the help. <BR>\n" );
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document.write( "Yes, it's possible but the coefficients are messy.<BR>\n" );
document.write( "This is a quadratic in term of x^3, that is, it's<BR>\n" );
document.write( "7.08(x^3)^2 + 4.15(x^3) - 9.6 = 0<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=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.08x%5E2%2B4.15x%2B-9.6+=+0 ALIGN=MIDDLE  ALT=\"7.08x%5E2%2B4.15x%2B-9.6+=+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=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%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=%284.15%29%5E2-4%2A7.08%2A-9.6=289.0945 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%284.15%29%5E2-4%2A7.08%2A-9.6=289.0945\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=289.0945 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+=+%28-4.15%2B-sqrt%28+289.0945+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-4.15%2B-sqrt%28+289.0945+%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=x%5B1%5D+=+%28-%284.15%29%2Bsqrt%28+289.0945+%29%29%2F2%5C7.08+=+0.90768214580453 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%284.15%29%2Bsqrt%28+289.0945+%29%29%2F2%5C7.08+=+0.90768214580453\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%284.15%29-sqrt%28+289.0945+%29%29%2F2%5C7.08+=+-1.49384033789493 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%284.15%29-sqrt%28+289.0945+%29%29%2F2%5C7.08+=+-1.49384033789493\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.08x%5E2%2B4.15x%2B-9.6 ALIGN=MIDDLE  ALT=\"7.08x%5E2%2B4.15x%2B-9.6\"   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=7.08x%5E2%2B4.15x%2B-9.6+=+%28x-0.90768214580453%29%2A%28x--1.49384033789493%29 ALIGN=MIDDLE  ALT=\"7.08x%5E2%2B4.15x%2B-9.6+=+%28x-0.90768214580453%29%2A%28x--1.49384033789493%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 0.90768214580453, -1.49384033789493.\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+7.08%2Ax%5E2%2B4.15%2Ax%2B-9.6+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+7.08%2Ax%5E2%2B4.15%2Ax%2B-9.6+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "The onsite solver always divides out the coefficient of the highest order term, but you can use the quadratic equation to find the roots, then use them to factor the polynomial.\r<BR>\n" );
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document.write( "The factors are not integers. </SPAN>\n" );
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