document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1042746>Question 1042746</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the Factor Theorem to determine whether x - c is a factor of f(x).\r<BR>\n" );
document.write( "\n" );
document.write( "8x3 + 36x2 - 19x - 5; x + 5<BR>\n" );
document.write( "    a. Yes<BR>\n" );
document.write( "    b. No<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #657774 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=657774\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x+5 is really x - (-5)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x - (-5) is in the form x - c where c = -5 in this case.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-----------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Remainder Theorem: if x - c is a factor of f(x), then f(c) = 0. This works both ways. If f(c) = 0, then x-c is a factor of f(x).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-----------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Use the remainder theorem to see if plugging x = -5 into f(x) yields 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = 8x^3 +36x^2 - 19x - 5<BR>\n" );
document.write( "y = 8(-5)^3 +36(-5)^2 - 19(-5) - 5<BR>\n" );
document.write( "y = 8(-125) +36(25) - 19(-5) - 5<BR>\n" );
document.write( "y = -1000 + 900 + 95 - 5<BR>\n" );
document.write( "y = -100 + 95 - 5<BR>\n" );
document.write( "y = -5 - 5<BR>\n" );
document.write( "y = -10\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The result is -10 which is NOT zero. Since it's not zero, this means that x+5 is NOT a factor of f(x).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Note: if you change y = 8x^3 +36x^2 - 19x - 5 to y = 8x^3 +36x^2 - 19x + 5, then x+5 would be a factor </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );