document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=697214>Question 697214</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For the polynomial below, -1 is a zero. \r<BR>\n" );
document.write( "\n" );
document.write( "f(x)=x^3 +5x^2 +17x +13\r<BR>\n" );
document.write( "\n" );
document.write( "Express f(x)  as a product of linear factors. \r<BR>\n" );
document.write( "\n" );
document.write( "f(x)= ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #429850 by </B><A HREF=/tutors/aboutme.mpl?userid=mouk><B>mouk(232)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mouk><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/cgi-bin/show-face.mpl?user=mouk><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=429850\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29=x%5E3+%2B5x%5E2+%2B17x+%2B13+ ALIGN=MIDDLE  ALT=\"+f%28x%29=x%5E3+%2B5x%5E2+%2B17x+%2B13+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If x=-1 is a root then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%2B1%29+ ALIGN=MIDDLE  ALT=\"+%28x%2B1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a factor so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29=%28x%2B1%29%28ax%5E2+%2B+bx+%2Bc%29+ ALIGN=MIDDLE  ALT=\"+f%28x%29=%28x%2B1%29%28ax%5E2+%2B+bx+%2Bc%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "By observation we can see the coefficient of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E3+ ALIGN=MIDDLE  ALT=\"+x%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is 1 so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+1+ ALIGN=MIDDLE  ALT=\"+a+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > so:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29=%28x%2B1%29%28x%5E2+%2B+bx+%2Bc%29+ ALIGN=MIDDLE  ALT=\"+f%28x%29=%28x%2B1%29%28x%5E2+%2B+bx+%2Bc%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29=%28x%5E3+%2B+bx%5E2+%2Bcx%29+%2B+%28x%5E2+%2B+bx+%2Bc%29+ ALIGN=MIDDLE  ALT=\"+f%28x%29=%28x%5E3+%2B+bx%5E2+%2Bcx%29+%2B+%28x%5E2+%2B+bx+%2Bc%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29=x%5E3+%2B+%28b%2B1%29x%5E2+%2B+%28c%2Bb%29x+%2B+c+ ALIGN=MIDDLE  ALT=\"+f%28x%29=x%5E3+%2B+%28b%2B1%29x%5E2+%2B+%28c%2Bb%29x+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Comparing coefficients of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E0+ ALIGN=MIDDLE  ALT=\"+x%5E0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c=13+ ALIGN=MIDDLE  ALT=\"+c=13+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Comparing coefficients of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+ ALIGN=MIDDLE  ALT=\"+x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%2B1=5+ ALIGN=MIDDLE  ALT=\"+b%2B1=5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b=4+ ALIGN=MIDDLE  ALT=\"+b=4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Comparing coefficients of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E1+ ALIGN=MIDDLE  ALT=\"+x%5E1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c%2Bb=17+ ALIGN=MIDDLE  ALT=\"+c%2Bb=17+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and is consistent with above\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Hence, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29=%28x%2B1%29%28x%5E2+%2B+4x+%2B+13%29+ ALIGN=MIDDLE  ALT=\"+f%28x%29=%28x%2B1%29%28x%5E2+%2B+4x+%2B+13%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This does not factorize further<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );