document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=69410>Question 69410</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534494498/algebrahomeworkh>Algebra & Trigonometry with Geometry</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Studying for final exam and require assistance with the following problems:\r<BR>\n" );
document.write( "\n" );
document.write( "If f(x)=x(x+3)(x-1), use interval notation to give all values of x where f(x)>0.\r<BR>\n" );
document.write( "\n" );
document.write( "If f(x)=x(x-1)(x-4)^2, use interval notation to give all values of x where f(x)>0.\r<BR>\n" );
document.write( "\n" );
document.write( "Find the quotient and remainder of f(x)=x^3-4x^2+5x+5 divided by p(x)=x-1.\r<BR>\n" );
document.write( "\n" );
document.write( "Find the quotient and remainder of f(x)=x^4-2 divided by p(x)=x-1.\r<BR>\n" );
document.write( "\n" );
document.write( "Stressing out please help... Thanks, John  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #49435 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=49435\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If f(x)=x(x+3)(x-1), use interval notation to give all values of x where f(x)>0.<BR>\n" );
document.write( "The product is zero when x=-3 or x=0 or x=1<BR>\n" );
document.write( "Draw a number line and put those values in the proper order on the line.<BR>\n" );
document.write( "You now have four intervals to look at.  Find a value in each interval<BR>\n" );
document.write( "as a test interval to see in what intervals the product is greater than zero.<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "Interval (-inf,-3); pick x=-100;  then f(x)= (-)(-)(-) which is <0<BR>\n" );
document.write( "Interval (-3,0); pick x= -2 ; then f(x)= (-)(+)(-) which is >0<BR>\n" );
document.write( "Interval (0,1) ; pick x= 1/2  ; then f(x)= (+)(+)(-) which is <0<BR>\n" );
document.write( "Interval (1,inf); pick x = 100; then f(x)= (+)(+)(+) which is >0<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "From this you see the answer is : (-3,0) or (1,inf)<BR>\n" );
document.write( "================================================================\r<BR>\n" );
document.write( "\n" );
document.write( "If f(x)=x(x-1)(x-4)^2, use interval notation to give all values of x where <BR>\n" );
document.write( "f(x)>0<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "Same procedure as above using x=0,x=1,x=4 <BR>\n" );
document.write( "==========================<BR>\n" );
document.write( "Find the quotient and remainder of f(x)=x^3-4x^2+5x+5 divided by p(x)=x-1.<BR>\n" );
document.write( "Use synthetic division :<BR>\n" );
document.write( "1)....1....-4....5....5<BR>\n" );
document.write( "........1....-3...2..| 7<BR>\n" );
document.write( "Quotient = x^2-3x+2<BR>\n" );
document.write( "Remainder = 7<BR>\n" );
document.write( "---------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( "Find the quotient and remainder of f(x)=x^4-2 divided by p(x)=x-1<BR>\n" );
document.write( "Use synthetic division:<BR>\n" );
document.write( "1)....1,,,,0....0....0....-2<BR>\n" );
document.write( "........1....1....1....1..|..-1\r<BR>\n" );
document.write( "\n" );
document.write( "Quotient: x^3+x^2+x+1<BR>\n" );
document.write( "Remainder: -1<BR>\n" );
document.write( "===========================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );