document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=76274>Question 76274</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the ac test to determine which of the following trinomials can be factored. Find the values of m and n for each trinomial that can be factored.\r<BR>\n" );
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document.write( "x(squared) + 2x - 15\r<BR>\n" );
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document.write( "thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #55126 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=55126\">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%2B2%2Ax%2B-15 ALIGN=MIDDLE  ALT=\"1%2Ax%5E2%2B2%2Ax%2B-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >, first we need to ask ourselves: What two numbers multiply to -15 and add to 2? Lets find out by listing all of the possible factors of -15<BR>\n" );
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document.write( "  Factors:<BR>\n" );
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document.write( "  1,3,5,15,<BR>\n" );
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document.write( "  -1,-3,-5,-15,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 -15.<BR>\n" );
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document.write( "  (-1)*(15)=-15<BR>\n" );
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document.write( "  (-3)*(5)=-15<BR>\n" );
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document.write( "   Now which of these pairs add to 2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 2<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 >-15</TD>|</TD><TD >|</TD><TD >1+(-15)=-14</TD></TR><TR><TD >3</TD><TD >|</TD><TD >-5</TD>|</TD><TD >|</TD><TD >3+(-5)=-2</TD></TR><TR><TD >-1</TD><TD >|</TD><TD >15</TD>|</TD><TD >|</TD><TD >(-1)+15=14</TD></TR><TR><TD >-3</TD><TD >|</TD><TD >5</TD>|</TD><TD >|</TD><TD >(-3)+5=2</TD></TR><TABLE>We can see from the table that -3 and 5 add to 2.So the two numbers that multiply to -15 and add to 2 are: -3 and 5\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=-3 and b=5\r\n" );
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document.write( "  So the equation becomes:\r\n" );
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document.write( "  (x-3)(x+5)\r\n" );
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document.write( "  Notice that if we foil (x-3)(x+5) we get the quadratic <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ax%5E2%2B2%2Ax%2B-15 ALIGN=MIDDLE  ALT=\"1%2Ax%5E2%2B2%2Ax%2B-15\"   DISABLED_style= \"max-width:90%; height:auto;\" > again</TD></TR>\n" );
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document.write( "So our polynomial factors to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%28x%2B5%29 ALIGN=MIDDLE  ALT=\"%28x-3%29%28x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%28x%2B5%29 ALIGN=MIDDLE  ALT=\"%28x-3%29%28x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > foils back to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x-15 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x-15\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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