document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=292578>Question 292578</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I  would appreciate assistance with how this problem is completed.\r<BR>\n" );
document.write( "\n" );
document.write( "In a study of worker efficiency at Wong<BR>\n" );
document.write( "Laboratories it was found that the number of components<BR>\n" );
document.write( "assembled per hour by the average worker t hours after<BR>\n" );
document.write( "starting work could be modeled by the formula<BR>\n" );
document.write( "N(t)=-3t^3+23t^2+8t.<BR>\n" );
document.write( "a) Rewrite the formula by factoring the right-hand side<BR>\n" );
document.write( "completely.<BR>\n" );
document.write( "b) Use the factored version of the formula to find N(3). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #211294 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=211294\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Equation is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-3t^3+23t^2+8t\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Factor by \"t\" to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "t * (-3t^2 + 23t + 8)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Set this equation equal to 0 to find the roots.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "t * (-3t^2 + 23t + 8) = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Factor (-3t^2 + 23t + 8) to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "t * (3t+1) * (-t+8) = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This makes t = 0 or (3t+1) = 0 or (-t+8) = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If 3t+1 = 0, then t = -1/3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If -t+8 = 0, then t = 8\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "or t = 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Your 3 possible roots are:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "t = -1/3<BR>\n" );
document.write( "t = 8<BR>\n" );
document.write( "t = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Plug these into your original equation to see if they are good.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Your original equation is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-3t^3+23t^2+8t\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "When t = 0, this equation becomes 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "When t = -1/3, this equation becomes -3*(-1/3)^3 + 23*(-1/3)^2 + 8*(-1/3).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This becomes .11111111 + 2.55555555 - 2.66666666 which becomes 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "When t = 8, this equation becomes -3*8^3 + 23*8^2 + 8*8.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This becomes -1536 + 1472 + 64 which becomes 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "All 3 roots are good.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Our factored equation is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "N(t) = t * (3t+1) * (-t+8) = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "When we substitute 3 for t, we get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "N(3) = 3 * (3*3+1) * (-3+8) which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "N(3) = 3 * 10 * 5 which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "N(3) = 150\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Plug 3 into the original equation of -3t^3+23t^2+8t and you get -3*(3^3) + 23*(3^2) + 8*3 which becomes -3*27 + 23*9 + 24 which becomes -81 + 207 + 24 which becomes 150.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The factoring is good and the answer is N(3) = 150\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I determined the factoring as follows:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I knew that 1*8 = 8 or 2*4 = 8 \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I tried 1*8 first.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I knew that 3*8 = 24 and -1*8 = -1 so I figured that the factors had to be something like (3t+1) * (-t+8)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "When you multiply these together, you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(3t+1) * (-t+8) =<BR>\n" );
document.write( "(3t * (-t+8)) + (1 * (-t+8)) =<BR>\n" );
document.write( "(-3t^2 + 24t) + (-t + 8) =<BR>\n" );
document.write( "-3t^2 + 24t -t + 8 = <BR>\n" );
document.write( "-3t^2 + 23t + 8 which makes them the correct factors.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );