document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=30879>Question 30879</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Factor completely<BR>\n" );
document.write( "2x^2 + 16x + 32<BR>\n" );
document.write( "x^3 + 3x^2 + x + 3<BR>\n" );
document.write( "3x^2 + 6x - 24 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #17620 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=17620\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x%5E2+%2B+16x+%2B+32+ ALIGN=MIDDLE  ALT=\"+2x%5E2+%2B+16x+%2B+32+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E3+%2B+3x%5E2+%2B+x+%2B+3+ ALIGN=MIDDLE  ALT=\"+x%5E3+%2B+3x%5E2+%2B+x+%2B+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You need to find a factor of this ie a value of x that makes the whole thing zero. Since all the terms are positive, then x must be a negative value, to make the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and x negative.\r<BR>\n" );
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document.write( "As to the value of x, well this is trial and error to find, but looking at the equation, the value -3 does jump out. Put x=-3 into the expression and you do get zero. So, x+3 is a factor.\r<BR>\n" );
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document.write( "You now need to divide this into the cubic expression and then factorise the resulting quadratic, if possible. Having done this for you, the final answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%28x%5E2%2B1%29 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%28x%5E2%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So try it.\r<BR>\n" );
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document.write( "Actually, there is a simpler method for this cubic: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E3+%2B+3x%5E2+%2B+x+%2B+3+ ALIGN=MIDDLE  ALT=\"+x%5E3+%2B+3x%5E2+%2B+x+%2B+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > written as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E3+%2B+x+%2B+3x%5E2+%2B+3+ ALIGN=MIDDLE  ALT=\"+x%5E3+%2B+x+%2B+3x%5E2+%2B+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Look the 2 sets of 2 terms and factorise each of those:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%5E3+%2B+x%29+%2B+%283x%5E2+%2B+3%29+ ALIGN=MIDDLE  ALT=\"+%28x%5E3+%2B+x%29+%2B+%283x%5E2+%2B+3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%28x%5E2+%2B+1%29+%2B+3%28x%5E2+%2B+1%29+ ALIGN=MIDDLE  ALT=\"+x%28x%5E2+%2B+1%29+%2B+3%28x%5E2+%2B+1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You can see that both halves have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B1 ALIGN=MIDDLE  ALT=\"x%5E2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so we can factorise again, as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%5E2+%2B+1%29%28x+%2B+3%29+ ALIGN=MIDDLE  ALT=\"+%28x%5E2+%2B+1%29%28x+%2B+3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Third example looks to be like the first.\r<BR>\n" );
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document.write( "jon.<BR>\n" );
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