document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=953637>Question 953637</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve each polynomial equation by factoring:<BR>\n" );
document.write( "1. 4x^5 - 8x^3 + 4x = 0<BR>\n" );
document.write( "2. x^4 - 12x^2 = -36<BR>\n" );
document.write( "3. 4x^3 + 7x^2 - 5x = 6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #582422 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=582422\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E5+-8x%5E3+%2B+4x+=+0 ALIGN=MIDDLE  ALT=\"4x%5E5+-8x%5E3+%2B+4x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%28x%5E4+-2x%5E2+%2B+1%29+=+0 ALIGN=MIDDLE  ALT=\"4x%28x%5E4+-2x%5E2+%2B+1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%28x%5E2+-+1%29%5E2+=+0 ALIGN=MIDDLE  ALT=\"4x%28x%5E2+-+1%29%5E2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%28x%5E2+-+1%29%28x%5E2+-+1%29+=+0 ALIGN=MIDDLE  ALT=\"4x%28x%5E2+-+1%29%28x%5E2+-+1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%28x+-+1%29%28x%2B1%29%28x+-+1%29%28x%2B1%29+=+0 ALIGN=MIDDLE  ALT=\"4x%28x+-+1%29%28x%2B1%29%28x+-+1%29%28x%2B1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+=+0 ALIGN=MIDDLE  ALT=\"4x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=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=%28x+-+1%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+-+1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >...double solution since we have factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1 ALIGN=MIDDLE  ALT=\"x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > twice<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29+=+0 ALIGN=MIDDLE  ALT=\"%28x%2B1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >...double solution since we have factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1 ALIGN=MIDDLE  ALT=\"x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > twice\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C4x%5E5+-8x%5E3+%2B+4x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C4x%5E5+-8x%5E3+%2B+4x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4+-12x%5E2+=+-36 ALIGN=MIDDLE  ALT=\"x%5E4+-12x%5E2+=+-36\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4+-12x%5E2+%2B36=0 ALIGN=MIDDLE  ALT=\"x%5E4+-12x%5E2+%2B36=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.............recall the rule <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a-b%29%5E2=a%5E2-2ab%2Bb%5E2 ALIGN=MIDDLE  ALT=\"%28a-b%29%5E2=a%5E2-2ab%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >; in your case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ab=12 ALIGN=MIDDLE  ALT=\"2ab=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=6 ALIGN=MIDDLE  ALT=\"b=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "now write it as a square of difference\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-6%29%5E2=0 ALIGN=MIDDLE  ALT=\"%28x%5E2+-6%29%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-6%29%28x%5E2+-6%29=0 ALIGN=MIDDLE  ALT=\"%28x%5E2+-6%29%28x%5E2+-6%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...since factors are same, you will have two pairs of double roots\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-6%29=0 ALIGN=MIDDLE  ALT=\"%28x%5E2+-6%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=6 ALIGN=MIDDLE  ALT=\"x%5E2=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%286%29 ALIGN=MIDDLE  ALT=\"x=sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-+sqrt%286%29 ALIGN=MIDDLE  ALT=\"x=-+sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > exact solution\r<BR>\n" );
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document.write( "=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2.5 ALIGN=MIDDLE  ALT=\"x=2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-+2.5 ALIGN=MIDDLE  ALT=\"x=-+2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > approximate\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+50%2C%28x%5E2+-6%29%28x%5E2+-6%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+50%2C%28x%5E2+-6%29%28x%5E2+-6%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "3. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E3+%2B+7x%5E2+-5x+=+6 ALIGN=MIDDLE  ALT=\"4x%5E3+%2B+7x%5E2+-5x+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E3+%2B+7x%5E2+-5x+-6=0 ALIGN=MIDDLE  ALT=\"4x%5E3+%2B+7x%5E2+-5x+-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E3-x%5E2%2B8x%5E2-2x-3x-6=0 ALIGN=MIDDLE  ALT=\"4x%5E3-x%5E2%2B8x%5E2-2x-3x-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%5E3%2B8x%5E2%29-%28x%5E2%2B2x%29-%283x%2B6%29=0 ALIGN=MIDDLE  ALT=\"%284x%5E3%2B8x%5E2%29-%28x%5E2%2B2x%29-%283x%2B6%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%28x%2B2%29-x%28x%2B2%29-3%28x%2B2%29=0 ALIGN=MIDDLE  ALT=\"4x%5E2%28x%2B2%29-x%28x%2B2%29-3%28x%2B2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%5E2-x-3%29%28x%2B2%29=0 ALIGN=MIDDLE  ALT=\"%284x%5E2-x-3%29%28x%2B2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%284x%5E2-4x%29%2B%283x-3%29%29%28x%2B2%29=0 ALIGN=MIDDLE  ALT=\"%28%284x%5E2-4x%29%2B%283x-3%29%29%28x%2B2%29=0\"   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=%284x%28x-1%29%2B3%28x-1%29%29%28x%2B2%29=0 ALIGN=MIDDLE  ALT=\"%284x%28x-1%29%2B3%28x-1%29%29%28x%2B2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%2B3%29%28x-1%29%28x%2B2%29=0 ALIGN=MIDDLE  ALT=\"%284x%2B3%29%28x-1%29%28x%2B2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B3=0 ALIGN=MIDDLE  ALT=\"4x%2B3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x=-3 ALIGN=MIDDLE  ALT=\"4x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2F4 ALIGN=MIDDLE  ALT=\"x=-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29=0 ALIGN=MIDDLE  ALT=\"%28x-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C4x%5E3+%2B+7x%5E2+-5x+-6%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C4x%5E3+%2B+7x%5E2+-5x+-6%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );