document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=635576>Question 635576</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the factor theorem so show that x - a is a factor of:<BR>\n" );
document.write( " x^2(a-b)^3 + a^2(b-x) + b^2(x-a) .<BR>\n" );
document.write( "I would appreciate it if you could help me with the steps. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #400414 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=400414\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the factor theorem to show that x - a is a factor of:<BR>\n" );
document.write( "x^2(a-b)^3 + a^2(b-x) + b^2(x-a) .<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "Factor Theorem:: x-a is a factor iff f(a) = 0.<BR>\n" );
document.write( "----<BR>\n" );
document.write( "f(x) = x^2(a-b)^3 + a^2(b-x) + b^2(x-a)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "f(a) = a^2(a-b)^3 + a^2(b-a) + b^2(a-a)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "= a^2(a-b)^3 - a^2(a-b) + 0<BR>\n" );
document.write( "---<BR>\n" );
document.write( "= a^2(a-b)[(a-b)^2-1]<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "That result does not satisfy the Factor Theorem requirement.<BR>\n" );
document.write( "x-a is NOT a factor of f(x)<BR>\n" );
document.write( "===============================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "===========   </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );