document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1174668>Question 1174668</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For what values of t can 10x^2+tx+8 be written as the product of two binomials?\r<BR>\n" );
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document.write( "I don't really get what we're supposed to do in this question. Please explain. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #800116 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52797)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=800116\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;According to the context, the coefficients of linear binomials are (should be) integer numbers.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Otherwise, &nbsp;the problem has &nbsp;INFINITELY &nbsp;MANY &nbsp;solutions.\r<BR>\n" );
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document.write( "Consider \r\n" );
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document.write( "    10x^2 + tx + 8 = (ax+b)*(cx+d).\r\n" );
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document.write( "Then we want to have  ac = 10,  bd = 8.\r\n" );
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document.write( "We have these cases\r\n" );
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document.write( "    a= 10, c= 1,  b= 8, d= 1;   (10x+8)*(1x+1) = 10x^2 + 18x + 8;   t = 18.\r\n" );
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document.write( "    a=  5, c= 2,  b= 8, d= 1;   ( 5x+8)*(2x+1) = 10x^2 + 21x + 8;   t = 21.\r\n" );
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document.write( "    a= -10, c= -1,  b= 8, d= 1;   (-10x+8)*(-1x+1) = 10x^2 - 18x + 8;  t = -18.\r\n" );
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document.write( "    a=  -5, c= -2,  b= 8, d= 1;   ( -5x+8)*(-2x+1) = 10x^2 + 21x + 8;  t = -21.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "It is only the beginning of an analysis.\r<BR>\n" );
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document.write( "The full number of cases is &nbsp;MUCH &nbsp;MORE.\r<BR>\n" );
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document.write( "I showed the idea to you.\r<BR>\n" );
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document.write( "Having a patience, &nbsp;you may continue and complete it &nbsp;ON &nbsp;YOUR &nbsp;OWN.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;REMEMBER:  &nbsp;you must satisfy two equalities  &nbsp;&nbsp;ac= 10,  &nbsp;&nbsp;bd= 8  &nbsp;in integer  numbers by trial and error; \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;try all appropriate positive and negative integer pairs.  &nbsp;Then for &nbsp;\"t\" &nbsp;you have this values  &nbsp;&nbsp;t = ad + bc.\r<BR>\n" );
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document.write( "I wish you pleasant pastime &nbsp;(!)\r<BR>\n" );
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document.write( "=============\r<BR>\n" );
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document.write( "Ignore the post by &nbsp;@josgarithmetic, &nbsp;since it is &nbsp;IRRELEVANT &nbsp;to the posed problem.\r<BR>\n" );
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document.write( "Do not distract yourself reading the post from  @MathLover1.\r<BR>\n" );
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document.write( "Learn from good sources (!) (!)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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