document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=816803>Question 816803</A>: <I><SPAN STYLE=\"word-break: break-all;\"> given f(x) is a factor of P(x); suppose that f(2) =0.  does that imply that P(2)=0?  why or why not? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #491733 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=491733\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since factors come in pairs, if f(x) is a factor of P(x) then there must be another factor. Let's call this other factor g(x). Then<BR>\n" );
document.write( "P(x) = f(x)*g(x)<BR>\n" );
document.write( "This means<BR>\n" );
document.write( "P(2) = f(2)*g(2)<BR>\n" );
document.write( "And since we know that f(2) = 0:<BR>\n" );
document.write( "P(2) = 0*g(2)<BR>\n" );
document.write( "From this we can see that it makes no difference what g(2) is. If you multiply it by 0 you get zero:<BR>\n" );
document.write( "P(2) = 0<BR>\n" );
document.write( "So yes, if a factor of P(2) is zero, then P(2) must be zero.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );