document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=112794>Question 112794</A>: <I><SPAN STYLE=\"word-break: break-all;\"> use the ac test to determine if trinomial is factored. find values of m and n.<BR>\n" );
document.write( "x^2-3x+7 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82222 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=82222\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I think you meant to say \"use the ac test to determine if the trinomial is factorable,\" and I'm presuming the m and n you are referring to are the m and n in the following:\r<BR>\n" );
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document.write( "First the AC method.  A and C refer to the coefficients on the equation in standard form, namely:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The first step of the AC method is to determine the product <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Ac ALIGN=MIDDLE  ALT=\"a%2Ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  In this case it is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2A7 ALIGN=MIDDLE  ALT=\"1%2A7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The second step of the AC method is to list the possible factor pairs of the product <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Ac ALIGN=MIDDLE  ALT=\"a%2Ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  In this case, 7 is a prime number so the only factor pairs that exist are (1,7) and (-1,-7).\r<BR>\n" );
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document.write( "The third step is to find a factor pair that adds up to b or -3 in this problem.  But there is no such pair because 1 + 7 = 8 and (-1) + (-7) = -8.  Therefore, the trinomial is not factorable.\r<BR>\n" );
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document.write( "Since the trinomial is not factorable, we are left with completing the square to find values for m and n in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Bm%29%28x%2Bn%29=x%5E2-3x%2B7 ALIGN=MIDDLE  ALT=\"%28x%2Bm%29%28x%2Bn%29=x%5E2-3x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Completeing the square:<BR>\n" );
document.write( "Step 1:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3x%2B7=0 ALIGN=MIDDLE  ALT=\"x%5E2-3x%2B7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Begin with the original trinomial set equal to zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3x=-7 ALIGN=MIDDLE  ALT=\"x%5E2-3x=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.   Add the negative of the constant term to both sides.  (if the coefficient on the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > term were other than 1, you would have the preliminary step of dividing both sides by that coefficient)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3x%2B%283%2F2%29%5E2=-7%2B%283%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2-3x%2B%283%2F2%29%5E2=-7%2B%283%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Take the coefficient on the x term, divide by 2 and then square the result and add that result to both sides of the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3x%2B%283%2F2%29%5E2=-19%2F4 ALIGN=MIDDLE  ALT=\"x%5E2-3x%2B%283%2F2%29%5E2=-19%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  And simplify the right side.\r<BR>\n" );
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document.write( "Now the left side of the equation is a perfect square that can be factored.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%2F2%29%5E2=-19%2F4 ALIGN=MIDDLE  ALT=\"%28x-3%2F2%29%5E2=-19%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F2%2B-sqrt%28-19%2F4%29 ALIGN=MIDDLE  ALT=\"x=3%2F2%2B-sqrt%28-19%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But we have a problem because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-1%29 ALIGN=MIDDLE  ALT=\"sqrt%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > doesn't exist.  So we define the imaginary number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i ALIGN=MIDDLE  ALT=\"i\"   DISABLED_style= \"max-width:90%; height:auto;\" > such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E2=-1 ALIGN=MIDDLE  ALT=\"i%5E2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Now we can write:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F2%2B-i%2Asqrt%2819%29%2F2 ALIGN=MIDDLE  ALT=\"x=3%2F2%2B-i%2Asqrt%2819%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, So,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F2%2Bi%2Asqrt%2819%29%2F2 ALIGN=MIDDLE  ALT=\"x=3%2F2%2Bi%2Asqrt%2819%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F2-i%2Asqrt%2819%29%2F2 ALIGN=MIDDLE  ALT=\"x=3%2F2-i%2Asqrt%2819%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is to say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-%283%2F2%2Bi%2Asqrt%2819%29%2F2%29=0 ALIGN=MIDDLE  ALT=\"x-%283%2F2%2Bi%2Asqrt%2819%29%2F2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-%283%2F2-i%2Asqrt%2819%29%2F2%29=0 ALIGN=MIDDLE  ALT=\"x-%283%2F2-i%2Asqrt%2819%29%2F2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  And now we can say that:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-%283%2F2%2Bi%2Asqrt%2819%29%2F2%29%29%28x-%283%2F2-i%2Asqrt%2819%29%2F2%29%29=x%5E2-3x%2B7 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > and finally,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-%283%2F2%2Bi%2Asqrt%2819%29%2F2%29 ALIGN=MIDDLE  ALT=\"m=-%283%2F2%2Bi%2Asqrt%2819%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=-%283%2F2-i%2Asqrt%2819%29%2F2%29 ALIGN=MIDDLE  ALT=\"n=-%283%2F2-i%2Asqrt%2819%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we still have to check the answer:\r<BR>\n" );
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document.write( "Is this statement true?  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-%283%2F2%2Bi%2Asqrt%2819%29%2F2%29%29%28x-%283%2F2-i%2Asqrt%2819%29%2F2%29%29=x%5E2-3x%2B7 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Apply the FOIL method to the left side:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-x%283%2F2-i%2Asqrt%2819%29%2F2%29-x%283%2F2%2Bi%2Asqrt%2819%29%2F2%29%2B%283%2F2%2Bi%2Asqrt%2819%29%2F2%29%283%2F2-i%2Asqrt%2819%29%2F2%29 ALIGN=MIDDLE   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=x%5E2-3x%2F2%2Bx%28i%2Asqrt%2819%29%2F2%29-3x%2F2-x%28i%2Asqrt%2819%29%2F2%29%2B9%2F4-3%28i%2Asqrt%2819%29%2F4%29%2B3%28i%2Asqrt%2819%29%2F4%29%2B19%2F4 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  Remembering that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E2=-1 ALIGN=MIDDLE  ALT=\"i%5E2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now collect terms and watch all of those pesky radicals go away:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3x%2B28%2F4 ALIGN=MIDDLE  ALT=\"x%5E2-3x%2B28%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3x%2B7 ALIGN=MIDDLE  ALT=\"x%5E2-3x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And the answer checks.\r<BR>\n" );
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document.write( "Hope this helps.\r<BR>\n" );
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document.write( "John </SPAN>\n" );
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