document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=198237>Question 198237</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395977258/algebrahomeworkh>algebra and trigonometry</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> find the values of a, b,c, and d that make the equation true.\r<BR>\n" );
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document.write( "(4t^3-at^2-2bt+5)-(ct^3+2t^2-6t+3) = t^3-2t+d </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #148688 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=148688\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284t%5E3-at%5E2-2bt%2B5%29-%28ct%5E3%2B2t%5E2-6t%2B3%29+=+t%5E3-2t%2Bd ALIGN=MIDDLE  ALT=\"%284t%5E3-at%5E2-2bt%2B5%29-%28ct%5E3%2B2t%5E2-6t%2B3%29+=+t%5E3-2t%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4t%5E3-at%5E2-2bt%2B5-ct%5E3-2t%5E2%2B6t-3+=+t%5E3-2t%2Bd ALIGN=MIDDLE  ALT=\"4t%5E3-at%5E2-2bt%2B5-ct%5E3-2t%5E2%2B6t-3+=+t%5E3-2t%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4t%5E3-at%5E2-2bt-ct%5E3-2t%5E2%2B6t-2+=+t%5E3-2t%2Bd ALIGN=MIDDLE  ALT=\"4t%5E3-at%5E2-2bt-ct%5E3-2t%5E2%2B6t-2+=+t%5E3-2t%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284t%5E3-ct%5E3%29%2B%28-at%5E2-2t%5E2%29%2B%28-2bt%2B6t%29%2B%282%29+=+t%5E3-2t%2Bd ALIGN=MIDDLE  ALT=\"%284t%5E3-ct%5E3%29%2B%28-at%5E2-2t%5E2%29%2B%28-2bt%2B6t%29%2B%282%29+=+t%5E3-2t%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284-c%29t%5E3%28-a-2%29t%5E2%2B%28-2b%2B6%29t%2B2+=+t%5E3-2t%2Bd ALIGN=MIDDLE  ALT=\"%284-c%29t%5E3%28-a-2%29t%5E2%2B%28-2b%2B6%29t%2B2+=+t%5E3-2t%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the respective GCFs from each group\r<BR>\n" );
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document.write( "Since the coefficient of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E3 ALIGN=MIDDLE  ALT=\"t%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the left side is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4-c ALIGN=MIDDLE  ALT=\"4-c\"   DISABLED_style= \"max-width:90%; height:auto;\" > and on the right side is 1, this means that we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4-c=1 ALIGN=MIDDLE  ALT=\"4-c=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Because the coefficient for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2 ALIGN=MIDDLE  ALT=\"t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the left is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a-2 ALIGN=MIDDLE  ALT=\"-a-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. However, there is no <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2 ALIGN=MIDDLE  ALT=\"t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the right. So this means that the coefficient of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2 ALIGN=MIDDLE  ALT=\"t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the right is 0. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a-2=0 ALIGN=MIDDLE  ALT=\"-a-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Finally, the coefficients for the \"t\" terms on the left and right sides are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2b%2B6 ALIGN=MIDDLE  ALT=\"-2b%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > respectively. So this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2b%2B6=-2 ALIGN=MIDDLE  ALT=\"-2b%2B6=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Take note that the only constants on the left and right sides are \"2\" and \"d\". So we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=d ALIGN=MIDDLE  ALT=\"2=d\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=2 ALIGN=MIDDLE  ALT=\"d=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So all you need to do is solve the equations:\r<BR>\n" );
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document.write( "To find the values of 'a', 'b', and 'c'. I'll let you do that.\r<BR>\n" );
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