document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=870577>Question 870577</A>: <I><SPAN STYLE=\"word-break: break-all;\"> consider the polynomial P(x)=x^3+3x^2+(3-k)x+1-k where k is a constant.<BR>\n" );
document.write( "a, show that P(-1)=0 for any value of k.<BR>\n" );
document.write( "b, find all solution to the equation P(x)=0 if k=-1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #524959 by </B><A HREF=/tutors/aboutme.mpl?userid=math1239028><B>math1239028(4)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math1239028><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=524959\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> That's an easy one:\r<BR>\n" );
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document.write( "a. Just replace where x=-1:<BR>\n" );
document.write( "P(-1)=(-1)^3+3(-1)^2+(3-k)(-1)+1-k <=><BR>\n" );
document.write( "P(-1)=-1+3-3+k+1-k=0 => P(-1)=0\r<BR>\n" );
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document.write( "b. for k=-1: P(x)=0<BR>\n" );
document.write( "P(x)=x^3+3x^2+4x+2=0<BR>\n" );
document.write( "And then you solve this equation:<BR>\n" );
document.write( "x^3+3x^2+4x+2=0<BR>\n" );
document.write( "(x+1)(x^2+2x+2)=0<BR>\n" );
document.write( "x+1=0 or (x+1)^2=-1<BR>\n" );
document.write( "x=-1  or  x+1=i or x+1=-i<BR>\n" );
document.write( "____or  x=-1+i or x= -1-i\r<BR>\n" );
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document.write( "So, summing up, P(x)=0 if k=-1, for x=-1 or x=-1+i or x=-1-i. </SPAN>\n" );
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