document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=175202>Question 175202</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that (x+3) and (x-1) are both factors of the same expression x^3+ax^2-bx-a,find the values of the constants a and b.<BR>\n" );
document.write( "Determine the third factor or the expression. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #130276 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=130276\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given that (x+3) and (x-1) are both factors of the same expression x^3+ax^2-bx-a,find the values of the constants a and b.<BR>\n" );
document.write( "Determine the third factor or the expression.<BR>\n" );
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document.write( "If x-1 is a factor, f(1) = 0<BR>\n" );
document.write( "f(1) = 1^3 + a(1^2) - b(1) -a = 1 + a -b -a = 1-b = 0<BR>\n" );
document.write( "Therefore b = 1<BR>\n" );
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document.write( "If x+3 is a factor, f(-3) = 0<BR>\n" );
document.write( "f(-3) = (-3)^3 + a(-3)^2 - b(-3) -a = 0<BR>\n" );
document.write( "-27 + 9a +3b -a = 0<BR>\n" );
document.write( "Substitute b=1 and get<BR>\n" );
document.write( "-27 +8a + 3 = 0<BR>\n" );
document.write( "8a = 24<BR>\n" );
document.write( "a = 3<BR>\n" );
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document.write( "f(x) = x^3+ax^2-bx-a<BR>\n" );
document.write( "f(x) = x^3 + 3x^2 -x - 3<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "Use synthetic division to find the 3rd factor:<BR>\n" );
document.write( "1)....1....3....-1....-3<BR>\n" );
document.write( ".......1......4...3...|..0<BR>\n" );
document.write( "-3).....1......1..|..0\r<BR>\n" );
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document.write( "3rd factor: x + 1<BR>\n" );
document.write( "=========================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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