document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=901776>Question 901776</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Good day\r<BR>\n" );
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document.write( "I have something puzzling me for quite a while now\r<BR>\n" );
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document.write( "Let't take an example \r<BR>\n" );
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document.write( "In the quadratic equation\r<BR>\n" );
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document.write( "1.  72c2 + 24c - 16\r<BR>\n" );
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document.write( "The answer is (12c - 4) (6c + 4)\r<BR>\n" );
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document.write( "Firstly.. Why 12 and 6? why not something like 9 and 8<BR>\n" );
document.write( "Tried the formula with this example numbered as \"1.\"\r<BR>\n" );
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document.write( "Secondly.. How do I know from the equation \"72c2 + 24c - 16\" which bracket is going to get the \"+\" and which bracket is going to get the \"-\"\r<BR>\n" );
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document.write( "They explained it in school but I just can't remember the principles.\r<BR>\n" );
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document.write( "Kind Regards.\r<BR>\n" );
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document.write( "Stefan. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #546964 by </B><A HREF=/tutors/aboutme.mpl?userid=MathTherapy><B>MathTherapy(10552)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathTherapy><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=MathTherapy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=546964\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Good day\r<BR>\n" );
document.write( "\n" );
document.write( "I have something puzzling me for quite a while now\r<BR>\n" );
document.write( "\n" );
document.write( "Let't take an example \r<BR>\n" );
document.write( "\n" );
document.write( "In the quadratic equation\r<BR>\n" );
document.write( "\n" );
document.write( "1.  72c2 + 24c - 16\r<BR>\n" );
document.write( "\n" );
document.write( "The answer is (12c - 4) (6c + 4)\r<BR>\n" );
document.write( "\n" );
document.write( "Firstly.. Why 12 and 6? why not something like 9 and 8<BR>\n" );
document.write( "Tried the formula with this example numbered as \"1.\"\r<BR>\n" );
document.write( "\n" );
document.write( "Secondly.. How do I know from the equation \"72c2 + 24c - 16\" which bracket is going to get the \"+\" and which bracket is going to get the \"-\"\r<BR>\n" );
document.write( "\n" );
document.write( "They explained it in school but I just can't remember the principles.\r<BR>\n" );
document.write( "\n" );
document.write( "Kind Regards.\r<BR>\n" );
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document.write( "Stefan.<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72c%5E2+%2B+24c+-+16 ALIGN=MIDDLE  ALT=\"72c%5E2+%2B+24c+-+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The first thing, when factoring this trinomial is to factor out the GCF, which is 8. <BR>\n" );
document.write( "Thus, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72c%5E2+%2B+24c+-+16 ALIGN=MIDDLE  ALT=\"72c%5E2+%2B+24c+-+16\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%289c%5E2+%2B+3c+-+2%29 ALIGN=MIDDLE  ALT=\"8%289c%5E2+%2B+3c+-+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, after which, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9c%5E2+%2B+3c+-+2 ALIGN=MIDDLE  ALT=\"9c%5E2+%2B+3c+-+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > should be factored.<BR>\n" );
document.write( "Final factors: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%288%283c+%2B+2%29%283c+-+1%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%288%283c+%2B+2%29%283c+-+1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "It's confusing when c is the variable in the trinomial, so it's better to <BR>\n" );
document.write( "change <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72c%5E2+%2B+24c+-+16 ALIGN=MIDDLE  ALT=\"72c%5E2+%2B+24c+-+16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72x%5E2+%2B+24x+-+16 ALIGN=MIDDLE  ALT=\"72x%5E2+%2B+24x+-+16\"   DISABLED_style= \"max-width:90%; height:auto;\" >....same thing, just that the variable was changed from c to x.<BR>\n" );
document.write( "Without factoring out a GCF, and applying the \"ac\" method, we would need two factors with a product<BR>\n" );
document.write( "of - 1,152 (a * c, or 72 * - 16), and that SUM to \"b\" (+ 24). These factors are: + 48 and - 24.<BR>\n" );
document.write( "We now replace + 24x in the trinomial, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72x%5E2+%2B+24x+-+16 ALIGN=MIDDLE  ALT=\"72x%5E2+%2B+24x+-+16\"   DISABLED_style= \"max-width:90%; height:auto;\" > with + 48x - 24x. I hope you're following!!\r<BR>\n" );
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document.write( "Now, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72x%5E2+%2B+24x+-+16 ALIGN=MIDDLE  ALT=\"72x%5E2+%2B+24x+-+16\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72x%5E2+%2B+48x+-+24x+-+16 ALIGN=MIDDLE  ALT=\"72x%5E2+%2B+48x+-+24x+-+16\"   DISABLED_style= \"max-width:90%; height:auto;\" >. At this point, I'd switch the variable, x back to c,<BR>\n" );
document.write( "so we now have: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72c%5E2+%2B+48c+-+24c+-+16 ALIGN=MIDDLE  ALT=\"72c%5E2+%2B+48c+-+24c+-+16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The factors are now obtained by grouping the first two binomials, and then the last two binomials, so that results in: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24c%283c+%2B+2%29+-+8%283c+%2B+2%29 ALIGN=MIDDLE  ALT=\"24c%283c+%2B+2%29+-+8%283c+%2B+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and the final answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2824c+-+8%29%283c+%2B+2%29 ALIGN=MIDDLE  ALT=\"%2824c+-+8%29%283c+%2B+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is the same as your factors: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812c+-+4%29%286c+%2B+4%29 ALIGN=MIDDLE  ALT=\"%2812c+-+4%29%286c+%2B+4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Factoring these further, results in: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%288%283c+-+1%29%283c+%2B+2%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%288%283c+-+1%29%283c+%2B+2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the CORRECT factors.\r<BR>\n" );
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document.write( "However, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2824c+-+8%29%283c+%2B+2%29 ALIGN=MIDDLE  ALT=\"%2824c+-+8%29%283c+%2B+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812c+-+4%29%286c+%2B+4%29 ALIGN=MIDDLE  ALT=\"%2812c+-+4%29%286c+%2B+4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are incorrect as the GCF of the original polynomial should be obtained<BR>\n" );
document.write( "and factored out first. I only went this far to explain the procedure to determine the correct factors when<BR>\n" );
document.write( "leading-coefficient multiples such as 24, 36, 72, and others are part of polynomials that need to be factored.<BR>\n" );
document.write( "These and other leading-coefficient multiples pose a problem at times since they have as many as 4 or 5 sets of<BR>\n" );
document.write( "factors, and can be pretty tedious to factor correctly. </SPAN>\n" );
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