document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=199846>Question 199846</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hi!\r<BR>\n" );
document.write( "\n" );
document.write( "A polynomial P is given.<BR>\n" );
document.write( "P(x) = x^3 + 216\r<BR>\n" );
document.write( "\n" );
document.write( "(a) Find all zeros of P, real and complex.\r<BR>\n" );
document.write( "\n" );
document.write( "(b) Factor P completely. \r<BR>\n" );
document.write( "\n" );
document.write( "thanks for the homework help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #150253 by </B><A HREF=/tutors/aboutme.mpl?userid=RAY100><B>RAY100(1637)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=RAY100><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=150253\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> great  problem<BR>\n" );
document.write( ".<BR>\n" );
document.write( "to  factor,,,,( x^3 +216),,,,first   examine  the  last  term  for  factors,  1,216, 2,108,3, 72, 4, 54, 6,36<BR>\n" );
document.write( ",<BR>\n" );
document.write( "now  we  try  to find  which  factor  will  go  evenly  into  the  function.,,,,usually  we  do  this  by  division,  either  polynomial  or  synthetic.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "using  synthetic  division  on  a  best  quess  of  (x+6) factor  or  x=-6  zero:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "-6,,,,,,,,,,,,,,1     0      0      216,,,,,,,,,,,,,,,,,,remember  to  fill  for  x^2  and  x terms<BR>\n" );
document.write( ",,,,,,,,,,,,,,,,,,,-6    36    -216<BR>\n" );
document.write( "______________________________<BR>\n" );
document.write( ",,,,,,,,,,,,,,1,,,-6,,,36,,,,,,,,0,,,,,,,,,,,,,,,as  remainder  is  zero,  this  is  a  factor<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(x+6) ( x^2 -6x +36),,,,,,,,,,,to  factor  the  second  term,  use  the  quadratic  formula<BR>\n" );
document.write( ".<BR>\n" );
document.write( "a= (1),,,,b=(-6) ,,,,,,c=(36)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "x =[ -(-6) +/- { (-6)^2 - 4 (1) (36) } ^(1/2) ] / 2 ( 1)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "x= [ 6 +/- { 36 -144)^(1/2) } ] /2<BR>\n" );
document.write( ".<BR>\n" );
document.write( "x= [ 6 +/- {-108)^(1/2) } ] /2,,,with  sqrt (-108)  = sqrt (-1) * sqrt (108 = 10.4 i<BR>\n" );
document.write( ".<BR>\n" );
document.write( "x= 3 +/- ( 5.2 i ),  x= 3+5.2i ,,,,,or  x = 3-5.2i<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Collecting  all  the  zeros,,,,x= (-6),,,, ( 3+5.2i) ,,,,,(3-5.2i)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "checking  <BR>\n" );
document.write( ".<BR>\n" );
document.write( "( x+6) ( x-(3+5.2i) )  ( x-(3-5.2i) )<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(x+6) ( x-3-5.2i) ( x-3+5.2i),,,,,good  summary  of  all  factors<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(x+6) ( x^2 -6x +36)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "x^3 + 216,,,,,ok </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );