document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=583198>Question 583198</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Question: Use the Rational Zeros Theorem to find all the real zeros of the polynomial function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+x%5E4+-+x%5E3-6x%5E2%2B4x%2B8 ALIGN=MIDDLE  ALT=\"f%28x%29+=+x%5E4+-+x%5E3-6x%5E2%2B4x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Use the zeros to factor f over the real numbers.\r<BR>\n" );
document.write( "\n" );
document.write( "I know the possible factors of the constant are 1, 2, 4, 8, -1, -2, -4, -8. But using the remainder theorem, none of them are actually possible factors (none of those factors have a remainder of 0). But when I graph it on a graphing calculator, there are zeros (x-intercepts). So I'm a little confused here. Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #372389 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=372389\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Question: Use the Rational Zeros Theorem to find all the real zeros of the polynomial function <BR>\n" );
document.write( "f(x) = x^4 - x^3-6x^2+4x+8. Use the zeros to factor f over the real numbers.<BR>\n" );
document.write( "**<BR>\n" );
document.write( "Rational Roots Theorem:<BR>\n" );
document.write( "Using synthetic division:<BR>\n" );
document.write( "...0....|.....1....-1.......-6.......4.....8<BR>\n" );
document.write( "...1....|.....1.....0.......-6.....-2....-8<BR>\n" );
document.write( "...2....|.....1.....1........-4....-4......0 (2 is a zero)<BR>\n" );
document.write( "=======================<BR>\n" );
document.write( "..,,0...|.....1..... 1......-4......-4<BR>\n" );
document.write( "..-1...|.....1......0.......-5......4<BR>\n" );
document.write( "..-2...|.....1.....-1.......-2.....0 (-2 is a zero)<BR>\n" );
document.write( "f(x)=(x-2)(x+2)(x^2-x-2)<BR>\n" );
document.write( "f(x)=(x-2)(x+2)(x-2)(x+1)<BR>\n" );
document.write( "Zeros: -2, -1, & 2 (multiplicity 2) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );