document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=330746>Question 330746</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Factor completely.  49a^2+4-28a </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #237120 by </B><A HREF=/tutors/aboutme.mpl?userid=neatmath><B>neatmath(302)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=neatmath><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=neatmath><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=237120\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49a%5E2%2B4-28a ALIGN=MIDDLE  ALT=\"49a%5E2%2B4-28a\"   DISABLED_style= \"max-width:90%; height:auto;\" > <br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49a%5E2-28a%2B4 ALIGN=MIDDLE  ALT=\"49a%5E2-28a%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "We must use the factors of the first term to see how this can be factored, using either 49 and 1, or 7 and 7.<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2849a-somenumber%29%28a-somenumber%29 ALIGN=MIDDLE  ALT=\"%2849a-somenumber%29%28a-somenumber%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287a-somenumber%29%287a-somenumber%29 ALIGN=MIDDLE  ALT=\"%287a-somenumber%29%287a-somenumber%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "Notice that both factors must have a negative sign in them, since the last term is positive, but the middle term is negative.<br>\r<BR>\n" );
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document.write( "Then we just have to use the factors of 4 to see what numbers will work to factor this. <br> \r<BR>\n" );
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document.write( "This is just a matter of guessing and checking, or trial and error.  Factors of 4 are 4 and 1, or 2 and 2.  So our answer MUST be one of the following, if this polynomial is factorable:<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2849a-4%29%28a-1%29 ALIGN=MIDDLE  ALT=\"%2849a-4%29%28a-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2849a-1%29%28a-4%29 ALIGN=MIDDLE  ALT=\"%2849a-1%29%28a-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2849a-2%29%2849a-2%29 ALIGN=MIDDLE  ALT=\"%2849a-2%29%2849a-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287a-4%29%287a-1%29 ALIGN=MIDDLE  ALT=\"%287a-4%29%287a-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287a-2%29%287a-2%29 ALIGN=MIDDLE  ALT=\"%287a-2%29%287a-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "Upon closer inspection, we can see that:<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287a-2%29%287a-2%29 ALIGN=MIDDLE  ALT=\"%287a-2%29%287a-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > does indeed multiply out to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49a%5E2-28a%2B4 ALIGN=MIDDLE  ALT=\"49a%5E2-28a%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "so the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287a-2%29%287a-2%29 ALIGN=MIDDLE  ALT=\"%287a-2%29%287a-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "This polynomial is a special one, in the form of:<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2-2ab%2Bb%5E2=%28a-b%29%5E2 ALIGN=MIDDLE  ALT=\"a%5E2-2ab%2Bb%5E2=%28a-b%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br> \r<BR>\n" );
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document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=7a ALIGN=MIDDLE  ALT=\"a=7a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=2 ALIGN=MIDDLE  ALT=\"b=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "Factoring polynomials is hard, and it takes a lot of practice.  There are also different ways to approach this problem, but I hope this helps! </SPAN>\n" );
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