document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=39580>Question 39580</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help! I feel like i'm up to my eyeballs in polynomials! I got a test and I need help with these 4 problems. #1 and #2 need to be factored. #3 and #4 need to be solved. Thanx =0) 1) 8x^3+8x-6x<BR>\n" );
document.write( "                        2) 24x^2-92x+80<BR>\n" );
document.write( "                        3) 6x^2+13x+6=0<BR>\n" );
document.write( "                        4) 2(a^2+9)=15a    </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #25030 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=25030\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) 8x^3+8x^2-6x<BR>\n" );
document.write( "=2x(4x^2+4x-3)<BR>\n" );
document.write( "=2x(2x-1)(2x+3)\r<BR>\n" );
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document.write( "2) 24x^2-92x+80<BR>\n" );
document.write( "4(6x^2-23x+20)<BR>\n" );
document.write( "=4(?)<BR>\n" );
document.write( "Use quadratic formula to get:<BR>\n" );
document.write( "x=[23+-sqrt(1009]/12<BR>\n" );
document.write( "=4(x-(23+sqrt(1009)]/12)(x-(23)-sqrt(1009))/12)<BR>\n" );
document.write( "3) 6x^2+13x+6=0<BR>\n" );
document.write( "x=[-13+-sqrt25]/12\r<BR>\n" );
document.write( "\n" );
document.write( "4) 2(a^2+9)=15a<BR>\n" );
document.write( "2a^2+18-15a=0<BR>\n" );
document.write( "2a^2-15a+18=0<BR>\n" );
document.write( "<TABLE  BORDER=1>\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=aa%5E2%2Bba%2Bc=0 ALIGN=MIDDLE  ALT=\"aa%5E2%2Bba%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%5E2%2B-15a%2B18+=+0 ALIGN=MIDDLE  ALT=\"2a%5E2%2B-15a%2B18+=+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=a%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"a%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=%28-15%29%5E2-4%2A2%2A18=81 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-15%29%5E2-4%2A2%2A18=81\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=81 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--15%2B-sqrt%28+81+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--15%2B-sqrt%28+81+%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=a%5B1%5D+=+%28-%28-15%29%2Bsqrt%28+81+%29%29%2F2%5C2+=+6 ALIGN=MIDDLE  ALT=\"a%5B1%5D+=+%28-%28-15%29%2Bsqrt%28+81+%29%29%2F2%5C2+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D+=+%28-%28-15%29-sqrt%28+81+%29%29%2F2%5C2+=+1.5 ALIGN=MIDDLE  ALT=\"a%5B2%5D+=+%28-%28-15%29-sqrt%28+81+%29%29%2F2%5C2+=+1.5\"   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=2a%5E2%2B-15a%2B18 ALIGN=MIDDLE  ALT=\"2a%5E2%2B-15a%2B18\"   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=2a%5E2%2B-15a%2B18+=+2%28a-6%29%2A%28a-1.5%29 ALIGN=MIDDLE  ALT=\"2a%5E2%2B-15a%2B18+=+2%28a-6%29%2A%28a-1.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 6, 1.5.\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+2%2Ax%5E2%2B-15%2Ax%2B18+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-15%2Ax%2B18+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "Hope this helps.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );