document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1075770>Question 1075770</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose $P(x)$ is a polynomial of smallest possible degree such that:\r<BR>\n" );
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document.write( "$\bullet$ $P(x)$ has rational coefficients\r<BR>\n" );
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document.write( "$\bullet$ $P(-3) = P(\sqrt 7) = P(1-\sqrt 6) = 0$\r<BR>\n" );
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document.write( "$\bullet$ $P(-1) = 8$\r<BR>\n" );
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document.write( "Determine the value of $P(0)$. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #690681 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=690681\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Rational coefficients and irrational roots means the irrational roots occur as conjugate pairs.<BR>\n" );
document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=a%28x%2B3%29%28x-sqrt%287%29%29%28x%2Bsqrt%287%29%29%28x-%281-sqrt%286%29%29%29%28x-%281%2Bsqrt%286%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=a%28x%2B3%29%28x%5E2-7%29%28x%5E2-2x-5%29 ALIGN=MIDDLE  ALT=\"P%28x%29=a%28x%2B3%29%28x%5E2-7%29%28x%5E2-2x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28-1%29=a%28-1%2B3%29%281-7%29%281%2B2-5%29 ALIGN=MIDDLE  ALT=\"P%28-1%29=a%28-1%2B3%29%281-7%29%281%2B2-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8=a%282%29%28-6%29%28-2%29 ALIGN=MIDDLE  ALT=\"8=a%282%29%28-6%29%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1%2F3 ALIGN=MIDDLE  ALT=\"a=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=%28%28x%2B3%29%28x%5E2-7%29%28x%5E2-2x-5%29%29%2F3 ALIGN=MIDDLE  ALT=\"P%28x%29=%28%28x%2B3%29%28x%5E2-7%29%28x%5E2-2x-5%29%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%280%29=%28%280%2B3%29%280-7%29%280-0-5%29%29%2F3 ALIGN=MIDDLE  ALT=\"P%280%29=%28%280%2B3%29%280-7%29%280-0-5%29%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%280%29=%28%283%29%28-7%29%28-5%29%29%2F3 ALIGN=MIDDLE  ALT=\"P%280%29=%28%283%29%28-7%29%28-5%29%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%280%29=35 ALIGN=MIDDLE  ALT=\"P%280%29=35\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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