document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=887448>Question 887448</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, \r<BR>\n" );
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document.write( "I have been having severe trouble with these polynomial/rational functions and would like help with this problem:\r<BR>\n" );
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document.write( "P(x) = 4x^4+4x^3+5x^2+4x+1 --> Directions: Find all the zeros of the polynomial. \r<BR>\n" );
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document.write( "--thank you to whomever decides to help me :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #536642 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=536642\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Because:<BR>\n" );
document.write( "P(x) = 4x^4+4x^3+5x^2+4x+1<BR>\n" );
document.write( "is a polynomial of degree 4, you must use synthetic division to reduce to a quadratic.<BR>\n" );
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document.write( "Possible zeros:<BR>\n" );
document.write( "1/4 = (+-) (1)/(1,2,4)<BR>\n" );
document.write( "possible zeros: +- 1, 1/2, 1/4<BR>\n" );
document.write( "try x=-1/2:<BR>\n" );
document.write( "-.5 | 4 4  5  4  1<BR>\n" );
document.write( "       -2 -1 -2 -1<BR>\n" );
document.write( "  ---------------<BR>\n" );
document.write( "      4 2  4  2  0<BR>\n" );
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document.write( "so, now you have:<BR>\n" );
document.write( "P(x) = (x+1/2)(4x^3+2x^2+4x+2)<BR>\n" );
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document.write( "possible zeros are (+-) factors of 2/4 <BR>\n" );
document.write( "try x = -1/2 <BR>\n" );
document.write( "-.5 | 4  2 4  2<BR>\n" );
document.write( "        -2 0 -2<BR>\n" );
document.write( "   -------------<BR>\n" );
document.write( "      4  0 4  0<BR>\n" );
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document.write( "so, now we have:<BR>\n" );
document.write( "P(x) = (x+1/2)(x+1/2)(4x^2+4)<BR>\n" );
document.write( "P(x) = 4(x+1/2)(x+1/2)(x^2+1)<BR>\n" );
document.write( "setting<BR>\n" );
document.write( "x^2+1 =0<BR>\n" );
document.write( "x^2 = -1<BR>\n" );
document.write( "x = {-i, i}<BR>\n" );
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document.write( "x = {-i, i, -1/2}  (two complex zeros and one real zero)<BR>\n" );
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