document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=267280>Question 267280</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having the worst time trying to solve this one. Here is what I have:\r<BR>\n" );
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document.write( "25x^2 + 10x + 1\r<BR>\n" );
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document.write( "I come up with (5x + 2)(5x   )<BR>\n" );
document.write( "and then i am lost!\r<BR>\n" );
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document.write( "Please help!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #196198 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=196198\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "First let's check to see if your factorization is correct.  We know that if we say that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\"> are the factors of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large c\">, then we must be able to multiply <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\"> times <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\"> and get <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large c\"> as a result.  Let's check your factors:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(5x\ +\ 2\right)\left(5x\right)\ =\ 25x^2\ +\ 10x\">\r<BR>\n" );
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document.write( "But you started with <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 25x^2\ +\ 10x\ +\ 1\"> and we can say for certain that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 25x^2\ +\ 10x\ +\ 1\ \neq\ 25x^2\ +\ 10x\"> (At least until someone invents a mathematics where 1 equals 0).\r<BR>\n" );
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document.write( "No wonder you are lost.\r<BR>\n" );
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document.write( "Let's see:  5 times 5 is 25, 1 times 1 is 1, and 5 plus 5 is 10.  So how about:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(5x\ +\ 1\right)\left(5x\ +\ 1\right)\">\r<BR>\n" );
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document.write( "Let's check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 5x\,\cdot\,5x\ =\ 25x^2\ \ \ \"> First\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 5x\,\cdot\,1\ =\ 5x\ \ \ \"> Outside\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 1\,\cdot\,5x\ =\ 5x\ \ \ \"> Inside\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 1\,\cdot\,1\ =\ 1\ \ \ \"> Last\r<BR>\n" );
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document.write( "Putting it all together:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 25x^2\ +\ 5x\ +\ 5x\ +\ 1\">\r<BR>\n" );
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document.write( "Collect like terms:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 25x^2\ +\ 10x\ +\ 1\">\r<BR>\n" );
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document.write( "Yep, that checks.  Your factors are indeed:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(5x\ +\ 1\right)\left(5x\ +\ 1\right)\">\r<BR>\n" );
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document.write( "Which can also be expressed:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(5x\ +\ 1\right)^2\">\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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