document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=449130>Question 449130</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please factorise the following:<BR>\n" );
document.write( "x^4 + 6x^3 + 8x^2 -6x + -9<BR>\n" );
document.write( "x-1 is a factor.<BR>\n" );
document.write( "i did, using long division divide polynomial by x-1 and i got x^3+7x^2+15x+9<BR>\n" );
document.write( "so my factors are (x-1)(x^3+7x^2+15x+9)<BR>\n" );
document.write( "now how can i factorise that further, do i i have to use long division or is there a quicker way?<BR>\n" );
document.write( "thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #308990 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=308990\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Can you please factorise the following:<BR>\n" );
document.write( "x^4 + 6x^3 + 8x^2 -6x + -9<BR>\n" );
document.write( "x-1 is a factor.<BR>\n" );
document.write( "i did, using long division divide polynomial by x-1 and i got x^3+7x^2+15x+9<BR>\n" );
document.write( "so my factors are (x-1)(x^3+7x^2+15x+9)<BR>\n" );
document.write( "now how can i factorise that further, do i  have to use long division or is there a quicker way?<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Look at the coefficients of the original problem.<BR>\n" );
document.write( "The sum of the coefficients is 1+6+8-6-9 = 0<BR>\n" );
document.write( "That means that x = 1 is a root; so x-1 is a factor.<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "Now look at x^3+7x^2+14x+9<BR>\n" );
document.write( "The sum of those coefficients is not zero, so x-1 is not a factor.<BR>\n" );
document.write( "But f(-1) = -1+7-15+9 = 0; so x = -1 is a zero, so x+1 is a factor.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "You have found two of the roots and can find the remaining roots <BR>\n" );
document.write( "using the Quadratic formula.<BR>\n" );
document.write( "-----------------------------------<BR>\n" );
document.write( "The fastest ways to find the Real Roots is to graph<BR>\n" );
document.write( "the problem with a graphing calculator.  The find<BR>\n" );
document.write( "the intersection of the problem with y = 0 to<BR>\n" );
document.write( "find the Real roots. Remember: if \"a\" is a root, x-a is a factor.<BR>\n" );
document.write( "=================================================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "==========<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );