document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177973>Question 1177973</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Find the value of k if (x^3-x^2-5x-2)(x^4+x^3+kx^2-5x+2)=x^7-4x^5-14x^4-5x^3+19x^2-4. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #807157 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=807157\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The answer can be obtained with FAR less work than shown by the other tutor....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E3-x%5E2-5x-2%29%28x%5E4%2Bx%5E3%2Bkx%5E2-5x%2B2%29=x%5E7-4x%5E5-14x%5E4-5x%5E3%2B19x%5E2-4 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "In the equation, k is the coefficient of the x^2 term.  So look at ANY one coefficient in the product of a term which is x^2 or a higher power of x.<br><BR>\n" );
document.write( "Example: The coefficient of the x^2 term in the product is 19.  That coefficient comes from (1) the constant term in the first expression times the x^2 term in the second, (2) the product of the linear terms in the two expressions, and (3) the x^2 term in the first expression and the constant term in the second:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19+=+%28-1%29%282%29%2B%28-5%29%28-5%29%2B%28-2%29%28k%29 ALIGN=MIDDLE  ALT=\"19+=+%28-1%29%282%29%2B%28-5%29%28-5%29%2B%28-2%29%28k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19+=+-2%2B25-2k ALIGN=MIDDLE  ALT=\"19+=+-2%2B25-2k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2k+=+4 ALIGN=MIDDLE  ALT=\"2k+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+2 ALIGN=MIDDLE  ALT=\"k+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: k=2<br><BR>\n" );
document.write( "I could have used any other coefficient of the product of a term with degree 2 or higher.<br><BR>\n" );
document.write( "Second example, using the coefficient of the x^4 term in the product:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-14+=+%281%29%28-5%29%2B%28-1%29%28k%29%2B%28-5%29%281%29%2B%28-2%29%281%29 ALIGN=MIDDLE  ALT=\"-14+=+%281%29%28-5%29%2B%28-1%29%28k%29%2B%28-5%29%281%29%2B%28-2%29%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-14+=+-5-k-5-2 ALIGN=MIDDLE  ALT=\"-14+=+-5-k-5-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+2 ALIGN=MIDDLE  ALT=\"k+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );