document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=152225>Question 152225</A>: <I><SPAN STYLE=\"word-break: break-all;\"> factor:  x^2-5x+6\r<BR>\n" );
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document.write( "thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #111889 by </B><A HREF=/tutors/aboutme.mpl?userid=nabla><B>nabla(475)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nabla><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=111889\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x^2-5x+6=(x-3)(x-2)\r<BR>\n" );
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document.write( "Explanation:\r<BR>\n" );
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document.write( "A 2nd degree polynomial (ax^2+bx+c) will factor, if factorisable, to form  (1) (dx+e)(fx+g). Now, if we apply foil to (1), we get eg+(ef+dg)x+df x^2\r<BR>\n" );
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document.write( "Now,<BR>\n" );
document.write( "eg=c<BR>\n" );
document.write( "ef+dg=b<BR>\n" );
document.write( "df=a\r<BR>\n" );
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document.write( "In words, we want two numbers e,g such that e*g equal the constant term of the original polynomial.\r<BR>\n" );
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document.write( "Moreover, we want numbers d,f such that d*f equals the coefficient of the x^2 term in the original polynomial.\r<BR>\n" );
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document.write( "Finally, we want two numbers f,d such that ef+dg equals the coefficient of the x term in the original polynomial.\r<BR>\n" );
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document.write( "As you can see, e and g give us the most useful information. We find e and g by looking at the factors of c.\r<BR>\n" );
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document.write( "For your polynomial, c is 6. The factors of 6 are 1,2,3,6. <BR>\n" );
document.write( "Now, for your polynomial, a is 1. 1 is the only factor of 1.\r<BR>\n" );
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document.write( "So we need numbers out of 1,2,3,6 that add to equal -5. We can see right away that -2+-3=-5. So these must be our f and g. So it factors as (x-3)(x-2) </SPAN>\n" );
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