document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=267263>Question 267263</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A polynomial in x has degree 3. The coefficient of x^2 is 3 less than the coefficient of x^3. The coefficient of x is three times the coefficient of x^2. The remaining coefficient is 2 more than the coefficient of x^3. The sum of the coefficients is -4. Find the polynomial. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #196282 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=196282\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We will try to get every variable in terms of a<BR>\n" );
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document.write( "A polynomial in x has degree 3.<BR>\n" );
document.write( "ax^3 + bx^2 + cx + d<BR>\n" );
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document.write( "The coefficient of x^2 is 3 less than the coefficient of x^3.<BR>\n" );
document.write( "b = a - 3<BR>\n" );
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document.write( "The coefficient of x is three times the coefficient of x^2.<BR>\n" );
document.write( "c = 3b<BR>\n" );
document.write( "Replace b with (a-3)<BR>\n" );
document.write( "c = 3(a-3)<BR>\n" );
document.write( "c = 3a - 9<BR>\n" );
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document.write( "The remaining coefficient is 2 more than the coefficient of x^3.<BR>\n" );
document.write( "d = a + 2<BR>\n" );
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document.write( "The sum of the coefficients is -4. Find the polynomial.<BR>\n" );
document.write( "a + b + c + d = -4<BR>\n" );
document.write( "Substitute, solve for a<BR>\n" );
document.write( "a + (a-3) + (3a-9) + (a+2) = -4<BR>\n" );
document.write( "6a - 10 = -4<BR>\n" );
document.write( "6a = -4 + 10<BR>\n" );
document.write( "6a = 6<BR>\n" );
document.write( "a = 1<BR>\n" );
document.write( "then<BR>\n" );
document.write( "b = 1 - 3<BR>\n" );
document.write( "b = -2<BR>\n" );
document.write( "and<BR>\n" );
document.write( "c = 3(1) - 9<BR>\n" );
document.write( "c = -6<BR>\n" );
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document.write( "d = 1 + 2<BR>\n" );
document.write( "d = 3<BR>\n" );
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document.write( "x^3 - 2x^2 - 6x + 3; is the polynomial<BR>\n" );
document.write( " </SPAN>\n" );
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