document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185631>Question 1185631</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A polynomial P is given.<BR>\n" );
document.write( "P(x) = x^4 + 18x^2 + 81<BR>\n" );
document.write( "(a) Factor P into linear and irreducible quadratic factors with real coefficients.<BR>\n" );
document.write( "(b) Factor P completely into linear factors with complex coefficients.\r<BR>\n" );
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document.write( "Find all zeros of the polynomial. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)\r<BR>\n" );
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document.write( "P(x) = 16x^4 + 16x^3 + 20x^2 + 16x + 4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #816467 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=816467\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "A polynomial P is given.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+x%5E4+%2B+18x%5E2+%2B+81 ALIGN=MIDDLE  ALT=\"P%28x%29+=+x%5E4+%2B+18x%5E2+%2B+81\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(a) Factor P into linear and irreducible quadratic factors with real coefficients.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+x%5E4+%2B+18x%5E2+%2B+81 ALIGN=MIDDLE  ALT=\"P%28x%29+=+x%5E4+%2B+18x%5E2+%2B+81\"   DISABLED_style= \"max-width:90%; height:auto;\" >....write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4 ALIGN=MIDDLE  ALT=\"x%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%5E2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81 ALIGN=MIDDLE  ALT=\"81\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%5E2 ALIGN=MIDDLE  ALT=\"9%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+%28x%5E2%29%5E2+%2B+18x%5E2%2B+9%5E2 ALIGN=MIDDLE  ALT=\"P%28x%29+=+%28x%5E2%29%5E2+%2B+18x%5E2%2B+9%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....recognize square of the sum\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+%28x%5E2++%2B9+%29%5E2 ALIGN=MIDDLE  ALT=\"P%28x%29+=+%28x%5E2++%2B9+%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(b) Factor P completely into linear factors with complex coefficients.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+%28x%5E2++%2B9+%29%5E2+ ALIGN=MIDDLE  ALT=\"P%28x%29+=+%28x%5E2++%2B9+%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+%28x%5E2++%2B9+%29%28x%5E2++%2B9+%29 ALIGN=MIDDLE  ALT=\"P%28x%29+=+%28x%5E2++%2B9+%29%28x%5E2++%2B9+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.............<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2++%2B9+=%28x+%2B+3i%29%28x+-+3i%29 ALIGN=MIDDLE  ALT=\"x%5E2++%2B9+=%28x+%2B+3i%29%28x+-+3i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=%28x+-+3i%29%5E2+%28x+%2B+3+i%29%5E2 ALIGN=MIDDLE  ALT=\"P%28x%29+=%28x+-+3i%29%5E2+%28x+%2B+3+i%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Find all zeros of the polynomial. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+16x%5E4+%2B+16x%5E3+%2B+20x%5E2+%2B+16x+%2B+4 ALIGN=MIDDLE  ALT=\"P%28x%29+=+16x%5E4+%2B+16x%5E3+%2B+20x%5E2+%2B+16x+%2B+4\"   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+=+4%284x%5E4+%2B+4x%5E3+%2B+5x%5E2+%2B+4x+%2B+1%29 ALIGN=MIDDLE  ALT=\"P%28x%29+=+4%284x%5E4+%2B+4x%5E3+%2B+5x%5E2+%2B+4x+%2B+1%29\"   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+=+4%284x%5E4+%2B+4x%5E3+%2B+4x%5E2%2Bx%5E2+%2B+4x+%2B+1%29 ALIGN=MIDDLE  ALT=\"P%28x%29+=+4%284x%5E4+%2B+4x%5E3+%2B+4x%5E2%2Bx%5E2+%2B+4x+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....group<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+4%28%284x%5E4+%2B+4x%5E2%29+%2B+%284x%5E3%2B+4x%29%2B%28x%5E2++%2B+1%29%29 ALIGN=MIDDLE  ALT=\"P%28x%29+=+4%28%284x%5E4+%2B+4x%5E2%29+%2B+%284x%5E3%2B+4x%29%2B%28x%5E2++%2B+1%29%29\"   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+=+4%284x%5E2%28x%5E2+%2B+1%29+%2B+4x%28x%5E2%2B+1%29%2B%28x%5E2++%2B+1%29%29 ALIGN=MIDDLE  ALT=\"P%28x%29+=+4%284x%5E2%28x%5E2+%2B+1%29+%2B+4x%28x%5E2%2B+1%29%2B%28x%5E2++%2B+1%29%29\"   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+=+4%284x%5E2+%2B+4x%2B1%29%28x%5E2++%2B+1%29 ALIGN=MIDDLE  ALT=\"P%28x%29+=+4%284x%5E2+%2B+4x%2B1%29%28x%5E2++%2B+1%29\"   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+=+4%28%282x%29%5E2+%2B+4x%2B1%29%28x%5E2++%2B+1%29 ALIGN=MIDDLE  ALT=\"P%28x%29+=+4%28%282x%29%5E2+%2B+4x%2B1%29%28x%5E2++%2B+1%29\"   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+=4%282x+%2B+1%29%5E2+%28x%5E2+%2B+1%29 ALIGN=MIDDLE  ALT=\"P%28x%29+=4%282x+%2B+1%29%5E2+%28x%5E2+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+1=0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=-1 ALIGN=MIDDLE  ALT=\"x%5E2+=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+i%29+%28x+%2B+i%29+ ALIGN=MIDDLE  ALT=\"%28x+-+i%29+%28x+%2B+i%29+\"   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+=4%28x+-+i%29+%28x+%2B+i%29+%282+x+%2B+1%29%5E2 ALIGN=MIDDLE  ALT=\"P%28x%29+=4%28x+-+i%29+%28x+%2B+i%29+%282+x+%2B+1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );