document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=374311>Question 374311</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to factor out this problem.  I am missing a step.  Can you explain how I factor? \r<BR>\n" );
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document.write( "5x^2+34x+24\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #266374 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=266374\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How to factor:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2%2B34x%2B24 ALIGN=MIDDLE  ALT=\"5x%5E2%2B34x%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To factor this trinomial, you need to find two binomials which, when multiplied, will give you the original trinomial.<BR>\n" );
document.write( "In other words, find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28ax%2Bm%29 ALIGN=MIDDLE  ALT=\"%28ax%2Bm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28bx%2Bn%29 ALIGN=MIDDLE  ALT=\"%28bx%2Bn%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28ax%2Bm%29%28bx%2Bn%29+=+5x%5E2%2B34x%2B24 ALIGN=MIDDLE  ALT=\"%28ax%2Bm%29%28bx%2Bn%29+=+5x%5E2%2B34x%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "First, you look at the coefficient of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and that's 5.<BR>\n" );
document.write( "Now ask what are the factors of 5?<BR>\n" );
document.write( "Well, 5 is a prime number, so the factors are 1 and 5.<BR>\n" );
document.write( "So you can start with:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%2Bm%29%28x%2Bn%29 ALIGN=MIDDLE  ALT=\"%285x%2Bm%29%28x%2Bn%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Notice the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=5 ALIGN=MIDDLE  ALT=\"a=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+1 ALIGN=MIDDLE  ALT=\"b+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now look at the constant term, that's 24.<BR>\n" );
document.write( "You need to find the two integers, m and n, whose product is 24 and whose sum 5*n+1*m = 34.<BR>\n" );
document.write( "Let's factor 24.<BR>\n" );
document.write( "1X24 = 24<BR>\n" );
document.write( "2X12 = 24<BR>\n" );
document.write( "3X8 = 24<BR>\n" );
document.write( "4X6 = 24<BR>\n" );
document.write( "After a little trial & error, you'll find:<BR>\n" );
document.write( "5*6+1*4 = 34<BR>\n" );
document.write( "So this means that n = 6 and m = 4<BR>\n" );
document.write( "Now you can finish by writing:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%285x%5E2%2B34x%2B24+=+%285x%2B4%29%28x%2B6%29%29 ALIGN=MIDDLE  ALT=\"highlight%285x%5E2%2B34x%2B24+=+%285x%2B4%29%28x%2B6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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