document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=27450>Question 27450</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Factor completely:<BR>\n" );
document.write( "x2 – 5x – 14\r<BR>\n" );
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document.write( "Factor completely:<BR>\n" );
document.write( "3x2 – 2x – 8\r<BR>\n" );
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document.write( "Factor completely:<BR>\n" );
document.write( "24x2 + 10x – 4<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 #14951 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=14951\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hint:  You can indicate x-squared by using the \"caret\", thus: x^2\r<BR>\n" );
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document.write( "Factor completely:<BR>\n" );
document.write( "1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-5x-14 ALIGN=MIDDLE  ALT=\"x%5E2-5x-14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If this trinomial expression factors, the factors will take the form: (x+m)(x+n) where: (m)*(n) = -14 and (m)+(n) = -5\r<BR>\n" );
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document.write( "Try m = -7 and n = +2\r<BR>\n" );
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document.write( "(2)(-7) = -14 and (2) + (-7) = -5\r<BR>\n" );
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document.write( "The factors are: (x-7)(x+2) Check using the FOIL method:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-7%29%28x%2B2%29+=+x%5E2%2B2x-7x-14 ALIGN=MIDDLE  ALT=\"%28x-7%29%28x%2B2%29+=+x%5E2%2B2x-7x-14\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-5x-14 ALIGN=MIDDLE  ALT=\"x%5E2-5x-14\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-2x-8 ALIGN=MIDDLE  ALT=\"3x%5E2-2x-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If this trinomial expression factors, the factors will take the form: (3x+m)(x+n) where: (m)*(n) = -8 and (m)+(3n) = -2\r<BR>\n" );
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document.write( "Try m = 4 and n = -2\r<BR>\n" );
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document.write( "(4)*(-2) = -8 and (4)+3(-2) = 4-6 = -2\r<BR>\n" );
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document.write( "The factors are: (3x+4)(x-2) Check using the FOIL method:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%2B4%29%28x-2%29+=+3x%5E2-6x%2B4x-8 ALIGN=MIDDLE  ALT=\"%283x%2B4%29%28x-2%29+=+3x%5E2-6x%2B4x-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-2x-8 ALIGN=MIDDLE  ALT=\"3x%5E2-2x-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24x%5E2%2B10x-4 ALIGN=MIDDLE  ALT=\"24x%5E2%2B10x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This one requires a little more work because of the lager number of possible factors of the coefficient of x^2 (24).<BR>\n" );
document.write( "First, list the factor-pairs of 24:<BR>\n" );
document.write( "1 X 24 = 24<BR>\n" );
document.write( "2 X 12 = 24<BR>\n" );
document.write( "3 X 8 = 24<BR>\n" );
document.write( "4 X 6 = 24\r<BR>\n" );
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document.write( "The choices of factors of the constant term in the given expression are:<BR>\n" );
document.write( "1 X -4 = -4<BR>\n" );
document.write( "-1 X 4 = -4<BR>\n" );
document.write( "2 X -2 = -4\r<BR>\n" );
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document.write( "Now you need to select a pair from the first list of factors and a pair from the second list of factors and, through an educated trial-and-error process, combine them to form the factors of the given expression.<BR>\n" );
document.write( "I would try 3 and 8 from the first list and 2 and -2 from the second list. Let's see what happens:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%2B2%29%288x-2%29+=+24x%5E2-6x%2B16x-4 ALIGN=MIDDLE  ALT=\"%283x%2B2%29%288x-2%29+=+24x%5E2-6x%2B16x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24x%5E2%2B10x-4 ALIGN=MIDDLE  ALT=\"24x%5E2%2B10x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Ok, a lucky(?) guess.\r<BR>\n" );
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