document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1031884>Question 1031884</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The polynomial f(x) has degree 3. If f(-1) = 15, f(0)= 0, f(1) = -5, and f(2) = 12, then what are the x-intercepts of the graph of f? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #646568 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=646568\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The polynomial f(x) has degree 3. If f(-1) = 15, f(0)= 0, f(1) = -5, and f(2) = 12, then what are the x-intercepts of the graph of f? <BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "Form:: ax^3 + bx^2 + cx + d = f(x)<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "Using f(-1) = 15: -a + b -c + d = 15<BR>\n" );
document.write( "Using f(0) = 0::: 0  + 0 + 0 + d = 0<BR>\n" );
document.write( "Using f(1) = -5:: a + b + c + d = -5<BR>\n" );
document.write( "Using f(2) = 12::8a + 4b + 2c +d = 12<BR>\n" );
document.write( "------------------------------------------<BR>\n" );
document.write( "Using d = 0 rewrite the equations:<BR>\n" );
document.write( "-a + b -c = 15<BR>\n" );
document.write( "a  + b +c = -5<BR>\n" );
document.write( "4a + 2b+c = 6<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "Add the top 2 equations to get:<BR>\n" );
document.write( "2b = 10<BR>\n" );
document.write( "b = 5<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Substitute the bottom two equations to get:<BR>\n" );
document.write( "3a + b = 11<BR>\n" );
document.write( "3a = 6<BR>\n" );
document.write( "a = 2<BR>\n" );
document.write( "----<BR>\n" );
document.write( "c = -5-a-b = -5-2-5 = -12<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "Equation:<BR>\n" );
document.write( "f(x) = 2x^3 + 5x^2 - 12x<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
document.write( "-------------- </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );