document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1126318>Question 1126318</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The function f is defined as f(x)=(x-2)(x+4)^2. Answer the following questions without using a graphing calculator.\r<BR>\n" );
document.write( "\n" );
document.write( "a. Use algebraic methods to determine the roots of f.\r<BR>\n" );
document.write( "\n" );
document.write( "b. On what interval(s) of x is f(x)positive? (Hint: enter \"U\" for &#8746; to combine more than one interval.)\r<BR>\n" );
document.write( "\n" );
document.write( "c. On what interval(s) of x is f(x)negative? (Hint: enter \"U\" for &#8746; to combine more than one interval.)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #742636 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=742636\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%28x-2%29%28x%2B4%29%5E2+=+%28x-2%29%28x%2B4%29%28x%2B4%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%28x-2%29%28x%2B4%29%5E2+=+%28x-2%29%28x%2B4%29%28x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The function value is 0 when any of the factors is 0 -- at x=-4 and at x=2.  The function value can change sign only at those two values.  So...<br><BR>\n" );
document.write( "(1) On (-infinity,-4), all three factors are negative, so the function value is negative.<BR>\n" );
document.write( "(2) On (-4,2) only one factor is negative, so the function value is again negative. (Both factors of (x+4) change sign at x=-4, so the function value remains negative.)<BR>\n" );
document.write( "(4) On (2,infinity) all three factors are positive, so the function value is positive. (At x=2, only one factor changes sign, so the function value changes sign.)<br><BR>\n" );
document.write( "So....<br><BR>\n" );
document.write( "ANSWERS:<BR>\n" );
document.write( "a. The roots are -4 and 2<BR>\n" );
document.write( "b. The function value is positive only on (2,infinity)<BR>\n" );
document.write( "c. The function value is negative on (-infinity,-4) U (-4,2) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );