document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=124326>Question 124326</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0130442631/algebrahomeworkh>Algebra 1</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Need to know how to solve 5x(squared)-26x+5 (factoring problem).  Page 301, problem #14.  The book is the California Edition </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #91141 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=91141\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given the following expression to factor:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2+-+26x+%2B+5 ALIGN=MIDDLE  ALT=\"5x%5E2+-+26x+%2B+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The 5 that is the multiplier of the <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;\" > has only two factors ... namely 5 and 1. So<BR>\n" );
document.write( "the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2+ ALIGN=MIDDLE  ALT=\"5x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > can only factor to 5x times 1x (or just 5x times x). This means the pair of<BR>\n" );
document.write( "factors must be of the form:<BR>\n" );
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document.write( "(5x +_____)*(x + _____)<BR>\n" );
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document.write( "The constant in the expression is also +5. It can factor into either +5 and +1 or into -5 and -1<BR>\n" );
document.write( "because in either case the product is +5. However, in the original expression, the middle term is<BR>\n" );
document.write( "negative. Therefore, we need to introduce a negative sign. This means that the factors of the<BR>\n" );
document.write( "+5 constant must be the pair -5 and -1. This means that our factors have two possibilities. They<BR>\n" );
document.write( "are either:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x+-5%29%2A%28x+-+1%29 ALIGN=MIDDLE  ALT=\"%285x+-5%29%2A%28x+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "or:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x+-+1%29%2A%28x+-+5%29 ALIGN=MIDDLE  ALT=\"%285x+-+1%29%2A%28x+-+5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If you multiply out the first set of factors the result is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2Ax+%2B+5x%28-1%29+%2B+%28-5%29%28x%29+%2B+%28-5%29%28-1%29+=+5x%5E2+-+5x+-5x+%2B+5+=+5x%5E2+-10x+%2B+5 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "That didn't work. So multiply out the second set of factors:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x+-+1%29%2A%28x+-+5%29+=+5x%2Ax+%2B+%285x%29%28-5%29+%2B+%28-1%29%28x%29+%2B+%28-1%29%28-5%29+=+5x%5E2+-+25x+-x+%2B+5+=+5x%5E2+-+26x+%2B5 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and that does work because the product is the same as the original expression you were given<BR>\n" );
document.write( "to factor.<BR>\n" );
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document.write( "So the answer to this problem is that the factored form of the original expression is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x+-+1%29%2A%28x+-+5%29 ALIGN=MIDDLE  ALT=\"%285x+-+1%29%2A%28x+-+5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better.<BR>\n" );
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