document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1100353>Question 1100353</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose f(x) is a polynomial.  What is the least possible degree of that polynomial?<BR>\n" );
document.write( "x: -24  -18  -12  -6  0  6  12  18  24<BR>\n" );
document.write( "f(x):  -8  -1  3  -2  4  7  -1  -8  5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #714857 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=714857\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>Every polynomial is a continuous function.<br><BR>\n" );
document.write( "The given value of f(x) show that the function value changes sign 5 times -- between -18 and -12, between -12 and -6, between -6 and 0, between 6 and 12, and between 18 and 24.<br><BR>\n" );
document.write( "Since the function is continuous and the function value changes sign 5 times, the function must have (at least) 5 zeros.<br><BR>\n" );
document.write( "Therefore the minimum degree of the polynomial is 5. </SPAN>\n" );
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