document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=978698>Question 978698</A>: <I><SPAN STYLE=\"word-break: break-all;\"> z^(4)-z^(2)-2z+2<BR>\n" );
document.write( "Please could someone help me with the last part of this question.\r<BR>\n" );
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document.write( "Write the following polynomial as products of linear factors:\r<BR>\n" );
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document.write( "z^(4)-z^(2)-2z+2\r<BR>\n" );
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document.write( "My try so far:\r<BR>\n" );
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document.write( "(z-1)(z^3+z^2-2)<BR>\n" );
document.write( "(z-1)(z-1)(z^2+z+2)\r<BR>\n" );
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document.write( "From here I tried to use the quadratic formula and got:<BR>\n" );
document.write( "Z=(-1+ sq rt 7)/2 or Z=(-1- sq rt 7)/2\r<BR>\n" );
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document.write( "The answer in the book is:\r<BR>\n" );
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document.write( "(z-1)^2 (z+1-i)(z+1+i)\r<BR>\n" );
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document.write( "Could anyone tell me where I went wrong?\r<BR>\n" );
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document.write( "Thank you for your time in advance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #600075 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=600075\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First try check for root of 1 gives  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28z-1%29%28z%5E3%2Bz%5E2-2%29 ALIGN=MIDDLE  ALT=\"%28z-1%29%28z%5E3%2Bz%5E2-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Be sure that your dividend of synthetic division shows ALL degrees of z.\r<BR>\n" );
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document.write( "continuing, again if root of 1 is checked, you find factorization <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28z-1%29%28z-1%29%28z%5E2%2B2z%2B2%29 ALIGN=MIDDLE  ALT=\"%28z-1%29%28z-1%29%28z%5E2%2B2z%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  You might have made a visual omission on paper or through keyboard, or maybe forgot about accounting for degrees of z in the division process.\r<BR>\n" );
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document.write( "NOW to deal with the quadratic factor,<BR>\n" );
document.write( "roots are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%2B-+sqrt%284-4%2A2%29%29%2F2 ALIGN=MIDDLE  ALT=\"%28-2%2B-+sqrt%284-4%2A2%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2B-+i ALIGN=MIDDLE  ALT=\"-1%2B-+i\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "To conitnue,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28z-1%29%5E2%28z-%28-1-i%29%29%28x-%28-1%2Bi%29%29 ALIGN=MIDDLE  ALT=\"%28z-1%29%5E2%28z-%28-1-i%29%29%28x-%28-1%2Bi%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and you simply simplify this obviously complex factorization or keep as linear and quadratic factorization...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28z-1%29%5E2%28z%2B1%2Bi%29%28z%2B1-i%29 ALIGN=MIDDLE  ALT=\"%28z-1%29%5E2%28z%2B1%2Bi%29%28z%2B1-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=highlight%28%28z-1%29%5E2%28%28z%2B1%29%2Bi%29%28%28z%2B1%29-i%29%29 ALIGN=MIDDLE  ALT=\"highlight%28%28z-1%29%5E2%28%28z%2B1%29%2Bi%29%28%28z%2B1%29-i%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Either you want it that way, or you want ...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28z-1%29%5E2%28z%5E2%2B2z%2B2%29%29 ALIGN=MIDDLE  ALT=\"highlight%28%28z-1%29%5E2%28z%5E2%2B2z%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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