document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171716>Question 1171716</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What are the number of possible values of b so that 4x² + bx - 9 can be factored as the product of two integral first degree polynomials? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #796645 by </B><A HREF=/tutors/aboutme.mpl?userid=Solver92311><B>Solver92311(821)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Solver92311><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=Solver92311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=796645\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "If the polynomial <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \rho(x)\ =\ 4x^2\,+\,bx\,-\,9\"> can be factored into integral first degree polynomials, then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{-b\,\pm\,\sqrt{b^2\,-\,(4)(4)(-9)}}{4}\,=\,\frac{-b\,\pm\,\sqrt{b^2\,+\,144}}{4}\,\in\ \mathbb{Q}\">\r<BR>\n" );
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document.write( "For that to be true, the radicand must be a perfect square and then both the sum and difference of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -b\"> and the radical must be evenly divisible by 4.  Hence, the allowable values of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\"> are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \{b\,|\,\sqrt{ b^2 \,+\,144}\,\in\,\mathbb{Q}\,&\,\(-b\,\pm\,\sqrt{b^2\,+\,144}\)\,\text{mod} \,4 \,= \, 0\}\">\r<BR>\n" );
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document.write( "The only number I can find that fits into that set is 16.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "From <https://www.algebra.com/cgi-bin/upload-illustration.mpl> <BR>\n" );
document.write( "I > Ø<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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