document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=76764>Question 76764</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Factor - \r<BR>\n" );
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document.write( "a2 +  4a - 45  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #55041 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=55041\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=factoring_quadratics.solver>Factoring Quadratics with a leading coefficient of 1 (a=1)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>In order to factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ax%5E2%2B4%2Ax%2B-45 ALIGN=MIDDLE  ALT=\"1%2Ax%5E2%2B4%2Ax%2B-45\"   DISABLED_style= \"max-width:90%; height:auto;\" >, first we need to ask ourselves: What two numbers multiply to -45 and add to 4? Lets find out by listing all of the possible factors of -45<BR>\n" );
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document.write( "  Factors:<BR>\n" );
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document.write( "  1,3,5,9,15,45,<BR>\n" );
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document.write( "  -1,-3,-5,-9,-15,-45,List the negative factors as well. This will allow us to find all possible combinations<BR>\n" );
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document.write( "  These factors pair up to multiply to -45.<BR>\n" );
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document.write( "  (-1)*(45)=-45<BR>\n" );
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document.write( "  (-3)*(15)=-45<BR>\n" );
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document.write( "  (-5)*(9)=-45<BR>\n" );
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document.write( "   Now which of these pairs add to 4? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 4<BR>\n" );
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document.write( "  <TABLE><TR><TD>First Number</TD><TD >|</TD><TD >Second Number</TD><TD >|</TD><TD >Sum</TD></TR><TR><TD >1</TD><TD >|</TD><TD >-45</TD>|</TD><TD >|</TD><TD >1+(-45)=-44</TD></TR><TR><TD >3</TD><TD >|</TD><TD >-15</TD>|</TD><TD >|</TD><TD >3+(-15)=-12</TD></TR><TR><TD >5</TD><TD >|</TD><TD >-9</TD>|</TD><TD >|</TD><TD >5+(-9)=-4</TD></TR><TR><TD >-1</TD><TD >|</TD><TD >45</TD>|</TD><TD >|</TD><TD >(-1)+45=44</TD></TR><TR><TD >-3</TD><TD >|</TD><TD >15</TD>|</TD><TD >|</TD><TD >(-3)+15=12</TD></TR><TR><TD >-5</TD><TD >|</TD><TD >9</TD>|</TD><TD >|</TD><TD >(-5)+9=4</TD></TR><TABLE>We can see from the table that -5 and 9 add to 4.So the two numbers that multiply to -45 and add to 4 are: -5 and 9\r\n" );
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document.write( "  Now we substitute these numbers into a and b of the general equation of a product of linear factors which is:\r\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Ba%29%28x%2Bb%29 ALIGN=MIDDLE  ALT=\"%28x%2Ba%29%28x%2Bb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >substitute a=-5 and b=9\r\n" );
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document.write( "  So the equation becomes:\r\n" );
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document.write( "  (x-5)(x+9)\r\n" );
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document.write( "  Notice that if we foil (x-5)(x+9) we get the quadratic <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ax%5E2%2B4%2Ax%2B-45 ALIGN=MIDDLE  ALT=\"1%2Ax%5E2%2B4%2Ax%2B-45\"   DISABLED_style= \"max-width:90%; height:auto;\" > again</TD></TR>\n" );
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document.write( "If we replace the x's with a's we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a-5%29%28a%2B9%29 ALIGN=MIDDLE  ALT=\"%28a-5%29%28a%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2B4a-45 ALIGN=MIDDLE  ALT=\"a%5E2%2B4a-45\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a-5%29%28a%2B9%29 ALIGN=MIDDLE  ALT=\"%28a-5%29%28a%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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