document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=181649>Question 181649</A>: <I><SPAN STYLE=\"word-break: break-all;\">  How do I factor this?             4x^3y^5z^2 - 12x^4y^6z^4 + 16x^2y^5z^3  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #136275 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=136275\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Factor:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math 4x^3y^5z^2 - 12x^4y^6z^4 + 16x^2y^5z^3\">\r<BR>\n" );
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document.write( "You can only extract a factor if it exists in all three terms.  So, for the numerical coefficients, you have 4, -12, and 16:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math 4 = 2 \times 2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math -12 = 2 \times 2 \times 3 \times -1\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math 16 = 2 \times 2 \times 2 \times 2\">\r<BR>\n" );
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document.write( "2 factors of 2 are common to all three, so take out <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2 \times 2 = 4\">\r<BR>\n" );
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document.write( "Leaving you with:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math 4(x^3y^5z^2 - 3x^4y^6z^4 + 4x^2y^5z^3)\">\r<BR>\n" );
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document.write( "All terms have at least 2 factors of <i>x</i>, so take out <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x^2\">, leaving you with:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math 4x^2(xy^5z^2 - 3x^2y^6z^4 + 4y^5z^3)\">\r<BR>\n" );
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document.write( "All terms have at least 5 factors of <i>y</i>, so take out <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y^5\">, leaving you with:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math 4x^2y^5(xz^2 - 3x^2yz^4 + 4z^3)\">\r<BR>\n" );
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document.write( "Finally, all terms have at least 2 factors of <i>z</i>, so take out <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large z^2\">, leaving you with:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math 4x^2y^5z^2(x - 3x^2yz^2 + 4z)\">\r<BR>\n" );
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document.write( "As your final answer.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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