document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=114212>Question 114212</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Factor the trinomail completely.\r<BR>\n" );
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document.write( "x squared - 11x - 60 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #83130 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=83130\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You want to factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-11x-60 ALIGN=MIDDLE  ALT=\"x%5E2-11x-60\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This is a trinomial of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > where a = 1, so we only have to consider the factors of c and the sum of those factors that equal b.\r<BR>\n" );
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document.write( "Step 1:\r<BR>\n" );
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document.write( "Look at the sign on the constant term.  In this case it is negative.  That means that the factors of -60 in this case must be of opposite signs.  Now we know that the factors of the trinomial are going to look like this:\r<BR>\n" );
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document.write( "(x + __ )\r<BR>\n" );
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document.write( "(x - __ )\r<BR>\n" );
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document.write( "Step 2:\r<BR>\n" );
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document.write( "We need to find two integers, call them p and q such that pq = -60 and p + q = -11.  Let's start with some possibilities:\r<BR>\n" );
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document.write( "p * q = -60<BR>\n" );
document.write( "-3 * 20 = -60 <BR>\n" );
document.write( "3 * -20 = -60  <BR>\n" );
document.write( "-4 * 15 = -60  <BR>\n" );
document.write( "4 * -15 = -60  <BR>\n" );
document.write( "-5 * 12 = -60<BR>\n" );
document.write( "5 * -12 = -60<BR>\n" );
document.write( "-6 * 10 = -60<BR>\n" );
document.write( "6 * -10 = -60\r<BR>\n" );
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document.write( "Step 3:\r<BR>\n" );
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document.write( "-3 + 20 = 17<BR>\n" );
document.write( "3 - 20 = -17<BR>\n" );
document.write( "-4 + 15 = 11<BR>\n" );
document.write( "4 - 15 = -11:  Ah Ha!\r<BR>\n" );
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document.write( "Now, for each of the choices of p and q above, which pair, when added together will yield -11?  The only pair that has a difference of 11 is 4 and 15, but since the result must be -11, the negative sign needs to be on the 15, so now we have our p and q and we can simply plug those numbers into our factor pattern we established in Step 1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%28x-15%29 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%28x-15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the required factorization.\r<BR>\n" );
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document.write( "Last step -- VERY IMPORTANT.  Check your answer.\r<BR>\n" );
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document.write( "Apply FOIL<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%28x-15%29=x%5E2-15x%2B4x-60=x%5E2-11x-60 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%28x-15%29=x%5E2-15x%2B4x-60=x%5E2-11x-60\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Checks.\r<BR>\n" );
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document.write( "Hope that helps,<BR>\n" );
document.write( "John </SPAN>\n" );
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