document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=133276>Question 133276</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write a polynomial function of least degree that has real coefficients, the given zeros and a leading coefficient of 1\r<BR>\n" );
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document.write( "18. 1,-3,4<BR>\n" );
document.write( "19. 2,2,-1,0<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #97482 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=97482\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If a polynomial has n zeros, it must be of degree n. (Fundamental Theorem of Algebra).  Also, if a is a zero of a polynomial equation, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-a ALIGN=MIDDLE  ALT=\"x-a\"   DISABLED_style= \"max-width:90%; height:auto;\" > must be a factor of the polynomial.\r<BR>\n" );
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document.write( "So, for problem 18, you have three zeros, so you must have three binomial factors that will expand to a 3rd degree polynomial.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%28x-%28-3%29%29%28x-4%29=%28x-1%29%28x%2B3%29%28x-4%29=%28x%5E2%2B2x-3%29%28x-4%29=x%5E3%2B2x%5E2-3x-4x%5E2-8x%2B12=x%5E3-2x%5E2-11x%2B12 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Do the other problem the same way, except that you have 4 zeros, so you will have 4 factors and a 4th degree polynomial at the end. </SPAN>\n" );
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