document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195206>Question 1195206</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If x+2 and x-3 are factors of the polynomial<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29=x%5E3%2B5x%5E2%2Bax%2Bb ALIGN=MIDDLE  ALT=\"p%28x%29=x%5E3%2B5x%5E2%2Bax%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >, find a. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #827640 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=827640\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "You have already received four responses, all showing different ways to solve the problem.<br><BR>\n" );
document.write( "Here is yet another way that might teach you something useful.<br><BR>\n" );
document.write( "In a cubic equation with leading coefficient 1,<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2Bbx%5E2%2Bcx%2Bd=0 ALIGN=MIDDLE  ALT=\"x%5E3%2Bbx%5E2%2Bcx%2Bd=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "with roots p, q, and r, the following are the relationships between the roots and the coefficients of the equation:<br><BR>\n" );
document.write( "(1) b = -(p+q+r)<BR>\n" );
document.write( "(2) c = (pq+pr+qr)<BR>\n" );
document.write( "(3) d = -(pqr)<br><BR>\n" );
document.write( "Note it is easy to see these relationships by writing the polynomial equation in factored form and expanding:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-p%29%28x-q%29%28x-r%29=x%5E3%2B%28-p-q-r%29x%5E2%2B%28pq%2Bpr%2Bqr%29x-pqr ALIGN=MIDDLE  ALT=\"%28x-p%29%28x-q%29%28x-r%29=x%5E3%2B%28-p-q-r%29x%5E2%2B%28pq%2Bpr%2Bqr%29x-pqr\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "To use these facts to solve this problem....<br><BR>\n" );
document.write( "Since x+2 and x-3 are factors of the polynomial, two of the roots are p=-2 and q=3.<br><BR>\n" );
document.write( "The coefficient of the x^2 term is 5, so from (1) above<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28p%2Bq%2Br%29=5 ALIGN=MIDDLE  ALT=\"-%28p%2Bq%2Br%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28%28-2%29%2B%283%29%2Br%29=5 ALIGN=MIDDLE  ALT=\"-%28%28-2%29%2B%283%29%2Br%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%281%2Br%29=5 ALIGN=MIDDLE  ALT=\"-%281%2Br%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Br=-5 ALIGN=MIDDLE  ALT=\"1%2Br=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=-6 ALIGN=MIDDLE  ALT=\"r=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So the third root is r=-6.<br><BR>\n" );
document.write( "The problem asks for the coefficient of the x (linear) term.  From (2) above, the coefficient of the linear term is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=pq%2Bpr%2Bqr=%28-2%29%283%29%2B%28-2%29%28-6%29%2B%283%29%28-6%29=-6%2B12-18=-12 ALIGN=MIDDLE  ALT=\"a=pq%2Bpr%2Bqr=%28-2%29%283%29%2B%28-2%29%28-6%29%2B%283%29%28-6%29=-6%2B12-18=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: a = -12<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );