document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=362440>Question 362440</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Im lost!\r<BR>\n" );
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document.write( "Solve the problem.\r<BR>\n" );
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document.write( "Find k such that f(x) = x4 + kx3 + 2 has the factor x + 1.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #258394 by </B><A HREF=/tutors/aboutme.mpl?userid=CharlesG2><B>CharlesG2(834)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CharlesG2><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=258394\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \"Im lost!\r<BR>\n" );
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document.write( "Solve the problem.\r<BR>\n" );
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document.write( "Find k such that f(x) = x4 + kx3 + 2 has the factor x + 1.\"\r<BR>\n" );
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document.write( "am sure this problem is f(x) = x^4 + kx^3 + 2, and we need to find k so that<BR>\n" );
document.write( "x + 1 is a factor\r<BR>\n" );
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document.write( "divide:<BR>\n" );
document.write( "          x^3 + (k - 1)x^2 - x + 1<BR>\n" );
document.write( "x + 1 --> x^4 + kx^3 + 2<BR>\n" );
document.write( "          x^4 + x^3<BR>\n" );
document.write( "               (k - 1)x^3       + 2<BR>\n" );
document.write( "               (k - 1)x^3 + x^2    <BR>\n" );
document.write( "                          - x^2     + 2<BR>\n" );
document.write( "                          - x^2 - x<BR>\n" );
document.write( "                                  x + 2<BR>\n" );
document.write( "                                  x + 1<BR>\n" );
document.write( "                                      1\r<BR>\n" );
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document.write( "x^3 + (k - 1)x^2 - x + 1 + 1/(x + 1) was result of division<BR>\n" );
document.write( "(x^3 + (k - 1)x^2 - x + 1 + 1/(x + 1))(x + 1)<BR>\n" );
document.write( "x^3(x + 1) + (k - 1)(x + 1)x^2 - x(x + 1) + x + 1 + 1<BR>\n" );
document.write( "x^4 + x^3 + (k - 1)(x^3 + x^2) - x^2 - x + x + 2<BR>\n" );
document.write( "x^4 + x^3 + kx^3 + kx^2 - x^3 - x^2 - x^2 + 2<BR>\n" );
document.write( "x^4 + kx^3 + kx^2 - 2x^2 + 2<BR>\n" );
document.write( "x^4 + kx^3 + (k - 2)x^2 + 2<BR>\n" );
document.write( "set k - 2 = 0<BR>\n" );
document.write( "k = 2<BR>\n" );
document.write( "to get x^4 + 2x^3 + 2\r<BR>\n" );
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document.write( "check:<BR>\n" );
document.write( "           x^3 + x^2 - x + 1<BR>\n" );
document.write( "x + 1  --> x^4 + 2x^3 + 2<BR>\n" );
document.write( "           x^4 + x^3<BR>\n" );
document.write( "                 x^3  + 2<BR>\n" );
document.write( "                 x^3  + x^2<BR>\n" );
document.write( "                      2 - x^2<BR>\n" );
document.write( "                     -x^2 - x<BR>\n" );
document.write( "                      2 + x<BR>\n" );
document.write( "                      x + 1<BR>\n" );
document.write( "                          1\r<BR>\n" );
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document.write( "                                   \r<BR>\n" );
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document.write( "              </SPAN>\n" );
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