document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=191471>Question 191471</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Factor the trinomial completely\r<BR>\n" );
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document.write( "3x^2-20x-7 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #143682 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=143682\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Looking at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-20x-7 ALIGN=MIDDLE  ALT=\"3x%5E2-20x-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can see that the first term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2 ALIGN=MIDDLE  ALT=\"3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the last term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7 ALIGN=MIDDLE  ALT=\"-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > where the coefficients are 3 and -7 respectively.\r<BR>\n" );
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document.write( "Now multiply the first coefficient 3 and the last coefficient -7 to get -21. Now what two numbers multiply to -21 and add to the  middle coefficient -20? Let's list all of the factors of -21:\r<BR>\n" );
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document.write( "Factors of -21:\r<BR>\n" );
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document.write( "1,3,7,21\r<BR>\n" );
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document.write( "-1,-3,-7,-21 ...List the negative factors as well. This will allow us to find all possible combinations\r<BR>\n" );
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document.write( "These factors pair up and multiply to -21\r<BR>\n" );
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document.write( "(1)*(-21)\r<BR>\n" );
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document.write( "(3)*(-7)\r<BR>\n" );
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document.write( "(-1)*(21)\r<BR>\n" );
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document.write( "(-3)*(7)\r<BR>\n" );
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document.write( "note: remember, the product of a negative and a positive number is a negative number\r<BR>\n" );
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document.write( "Now which of these pairs add to -20? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -20\r<BR>\n" );
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document.write( "<th>First Number</th><th>Second Number</th><th>Sum</th><tr><TD  align=\"center\">1</TD><TD  align=\"center\">-21</TD><TD >1+(-21)=-20</TD></tr><tr><TD  align=\"center\">3</TD><TD  align=\"center\">-7</TD><TD >3+(-7)=-4</TD></tr><tr><TD  align=\"center\">-1</TD><TD  align=\"center\">21</TD><TD >-1+21=20</TD></tr><tr><TD  align=\"center\">-3</TD><TD  align=\"center\">7</TD><TD >-3+7=4</TD></tr>\n" );
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document.write( "From this list we can see that 1 and -21 add up to -20 and multiply to -21\r<BR>\n" );
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document.write( "Now looking at the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-20x-7 ALIGN=MIDDLE  ALT=\"3x%5E2-20x-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-20x ALIGN=MIDDLE  ALT=\"-20x\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-21x ALIGN=MIDDLE  ALT=\"x-21x\"   DISABLED_style= \"max-width:90%; height:auto;\" > (notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-21x ALIGN=MIDDLE  ALT=\"x-21x\"   DISABLED_style= \"max-width:90%; height:auto;\" > combines to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-20x ALIGN=MIDDLE  ALT=\"-20x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So it is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-20x ALIGN=MIDDLE  ALT=\"-20x\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2Bhighlight%28x-21x%29-7 ALIGN=MIDDLE  ALT=\"3x%5E2%2Bhighlight%28x-21x%29-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2Bx-21x-7 ALIGN=MIDDLE  ALT=\"3x%5E2%2Bx-21x-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > by grouping:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%5E2%2Bx%29%2B%28-21x-7%29 ALIGN=MIDDLE  ALT=\"%283x%5E2%2Bx%29%2B%28-21x-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%283x%2B1%29-7%283x%2B1%29 ALIGN=MIDDLE  ALT=\"x%283x%2B1%29-7%283x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > out of the first group. Factor out the GCF of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7 ALIGN=MIDDLE  ALT=\"-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > out of the second group\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-7%29%283x%2B1%29 ALIGN=MIDDLE  ALT=\"%28x-7%29%283x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Since we have a common term of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B1 ALIGN=MIDDLE  ALT=\"3x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can combine like terms\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2Bx-21x-7 ALIGN=MIDDLE  ALT=\"3x%5E2%2Bx-21x-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-7%29%283x%2B1%29 ALIGN=MIDDLE  ALT=\"%28x-7%29%283x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So this also means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-20x-7 ALIGN=MIDDLE  ALT=\"3x%5E2-20x-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-7%29%283x%2B1%29 ALIGN=MIDDLE  ALT=\"%28x-7%29%283x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-20x-7 ALIGN=MIDDLE  ALT=\"3x%5E2-20x-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2Bx-21x-7 ALIGN=MIDDLE  ALT=\"3x%5E2%2Bx-21x-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "     Answer:\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-20x-7 ALIGN=MIDDLE  ALT=\"3x%5E2-20x-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-7%29%283x%2B1%29 ALIGN=MIDDLE  ALT=\"%28x-7%29%283x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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