document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=36349>Question 36349</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Here I need to factor the quadratic expression completely, and find the roots of the expression.\r<BR>\n" );
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document.write( "135x^2 - 222x + 91 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #22352 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=22352\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a hard one to factor but it can be done with a bit of trial & error:<BR>\n" );
document.write( "The factors of 135 are:<BR>\n" );
document.write( "1 X 135 = 135<BR>\n" );
document.write( "3 X 45 = 135<BR>\n" );
document.write( "5 X 27 = 135<BR>\n" );
document.write( "9 X 15 = 135<BR>\n" );
document.write( "The factors of 91 are:<BR>\n" );
document.write( "1 X 91 = 91<BR>\n" );
document.write( "7 X 13 = 91\r<BR>\n" );
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document.write( "You can try various combinations of these but the sum (or the difference) of the factors for the x-term must equal -222.<BR>\n" );
document.write( "For example:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815x+-+13%29%289x+-+7%29+=+135x%5E2+-+222x+%2B+91 ALIGN=MIDDLE  ALT=\"%2815x+-+13%29%289x+-+7%29+=+135x%5E2+-+222x+%2B+91\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To find the roots, we must have an equation, so you can set the expression equal to zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=135x%5E2+-+222x+%2B+91+=+0 ALIGN=MIDDLE  ALT=\"135x%5E2+-+222x+%2B+91+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815x+-+13%29%289x+-+7%29+=+0 ALIGN=MIDDLE  ALT=\"%2815x+-+13%29%289x+-+7%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Apply the zero products principle.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x+-+13+=+0 ALIGN=MIDDLE  ALT=\"15x+-+13+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and/or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x+-+7+=+0 ALIGN=MIDDLE  ALT=\"9x+-+7+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x+-+13+=+0 ALIGN=MIDDLE  ALT=\"15x+-+13+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x+=+13 ALIGN=MIDDLE  ALT=\"15x+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+13%2F15 ALIGN=MIDDLE  ALT=\"x+=+13%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x+-+7+=+0 ALIGN=MIDDLE  ALT=\"9x+-+7+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x+=+7 ALIGN=MIDDLE  ALT=\"9x+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+7%2F9 ALIGN=MIDDLE  ALT=\"x+=+7%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The factors are: (15x - 13) and (9x - 7)<BR>\n" );
document.write( "The roots are: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+13%2F15 ALIGN=MIDDLE  ALT=\"x+=+13%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+7%2F9 ALIGN=MIDDLE  ALT=\"x+=+7%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( " </SPAN>\n" );
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