document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=90319>Question 90319</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The problem says factor:\r<BR>\n" );
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document.write( "x^2-25\r<BR>\n" );
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document.write( "x^2-7x-12\r<BR>\n" );
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document.write( "I forgot how to factor these so maybe if you just explain it briefly I might remember,thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #65554 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=65554\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ah yes...factoring!!<BR>\n" );
document.write( "1) Factor:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+25 ALIGN=MIDDLE  ALT=\"x%5E2+-+25\"   DISABLED_style= \"max-width:90%; height:auto;\" > Look at each term and notice that they are both \"perfect squares\".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29%5E2+-+%285%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%29%5E2+-+%285%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This suggests that the factors will be of the form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+n%29%28x+-+n%29 ALIGN=MIDDLE  ALT=\"%28x+%2B+n%29%28x+-+n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which would get you <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+n%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+-+n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > when multiplied.<BR>\n" );
document.write( "So, in this case, n = 5 so the factors are:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-25+=+%28x%2B5%29%28x-5%29 ALIGN=MIDDLE  ALT=\"x%5E2-25+=+%28x%2B5%29%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2) Factor:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-7x-12 ALIGN=MIDDLE  ALT=\"x%5E2-7x-12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The factors will have the form: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Bm%29%28x%2Bn%29 ALIGN=MIDDLE  ALT=\"%28x%2Bm%29%28x%2Bn%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%2Bn+=+-7 ALIGN=MIDDLE  ALT=\"m%2Bn+=+-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%2An+=+-12 ALIGN=MIDDLE  ALT=\"m%2An+=+-12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The two numbers come to mind are 3 and 4 becuase:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2B4+=+7 ALIGN=MIDDLE  ALT=\"3%2B4+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A4+=+12 ALIGN=MIDDLE  ALT=\"3%2A4+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now all you have to do is to make sure the signs of the two numbers, n and m, will give the correct signs (negative, in this case) for the sum and the product.<BR>\n" );
document.write( "But, there is a problem!<BR>\n" );
document.write( "To get a product of -12, the 3 and the 4 must have opposite signs, right?<BR>\n" );
document.write( "But if the 3 and the 4 have opposite signs, then their sum can never be -7, can it?<BR>\n" );
document.write( "So, scrap the 3 and the 4.<BR>\n" );
document.write( "What other factors of 12 are there?<BR>\n" );
document.write( "-1*12 or 1*-12<BR>\n" );
document.write( "-2*6 or 2*-6<BR>\n" );
document.write( "Looking at these factors, there's no way you are going to get a sum -7<BR>\n" );
document.write( "So, you have to say that:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-7x-12 ALIGN=MIDDLE  ALT=\"x%5E2-7x-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > is prime! (Not factorable)<BR>\n" );
document.write( "Now if your expression had been:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-7x%2B12 ALIGN=MIDDLE  ALT=\"x%5E2-7x%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" > then you could factor this as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-7x%2B12+=+%28x-3%29%28x-4%29 ALIGN=MIDDLE  ALT=\"x%5E2-7x%2B12+=+%28x-3%29%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "But it isn't, so you can't!\r<BR>\n" );
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document.write( " </SPAN>\n" );
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