document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=175211>Question 175211</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the remainder when 3t^2+5t-7 is divided by t-5? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #130337 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=130337\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 3t^2 + 5t - 7 divided by t-5<BR>\n" );
document.write( "---<BR>\n" );
document.write( "t goes into 3t^2 by a factor of 3t.<BR>\n" );
document.write( "3t * (t-5) = 3t^2 - 15t<BR>\n" );
document.write( "---<BR>\n" );
document.write( "3t^2 + 5t - 7 minus 3t^2 - 15t equals 20t - 7<BR>\n" );
document.write( "---<BR>\n" );
document.write( "t goes into 20t by a factor of 20<BR>\n" );
document.write( "20 * (t-5) = 20t - 100<BR>\n" );
document.write( "---<BR>\n" );
document.write( "20t - 7 minus 20t - 100 equals 93<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the remainder is 93/(t-5)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the complete answer is 3t + 20 + 93/(t-5)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "to prove this is true, then (t-5) * (3t + 20 + 93/(t-5)) should equal 3t^2 + 5t - 7<BR>\n" );
document.write( "---<BR>\n" );
document.write( "when you multiply polynomials, each factor in one polynomial has to be multiplied by each factor in the other polynomial.<BR>\n" );
document.write( "this means that:<BR>\n" );
document.write( "(a + b) * (c + d + e) equals (ac + ad + ae) + (bc + bd + be) = first way<BR>\n" );
document.write( "alternatively, this also means that:<BR>\n" );
document.write( "(a + b) * (c + d + e) equals (ac + bc) + (ad + bd) + (ae + be) = second way<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the answer is the same either way.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "multiplying them out the first way, you get:<BR>\n" );
document.write( "(t-5) * (3t + 20 + 93/(t-5)) = t*(3t + 20 + 93/(t-5)) - 5*(3t + 20 + 93/(t-5))<BR>\n" );
document.write( "which equals<BR>\n" );
document.write( "3t^2 + 20t + 93t/(t-5) - 15t - 100 - 5*93/(t-5)<BR>\n" );
document.write( "which equals<BR>\n" );
document.write( "3t^2 + 5t - 100 + 93t/(t-5) - 5*93/(t-5)<BR>\n" );
document.write( "which equals<BR>\n" );
document.write( "3t^2 + 5t - 100 + 93*(t-5)/(t-5)<BR>\n" );
document.write( "which equals<BR>\n" );
document.write( "3t^2 + 5t - 100 + 93<BR>\n" );
document.write( "which equals<BR>\n" );
document.write( "3t^2 + 5t - 7<BR>\n" );
document.write( "---<BR>\n" );
document.write( "multiplying them out the second way, you get:<BR>\n" );
document.write( "(t-5) * (3t + 20 + 93/(t-5)) = (t-5) * 3t) + ((t-5) * 20) + (t-5)*93/(t-5)<BR>\n" );
document.write( "which equals<BR>\n" );
document.write( "3t^2 - 15t + 20t - 100 + 93<BR>\n" );
document.write( "which equals<BR>\n" );
document.write( "3t^2 + 5t - 7<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the answer is the same.<BR>\n" );
document.write( "the remainder is 93/(t-5)<BR>\n" );
document.write( "--- </SPAN>\n" );
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