document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=65544>Question 65544</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that (3x-a)(x-2)(x-7)=3x^3-32x^2+81x-70, determine the value of a...\r<BR>\n" );
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document.write( "HELP! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #46161 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=46161\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (1)  Given that (3x-a)(x-2)(x-7)=3x^3-32x^2+81x-70, determine the value of a...\r<BR>\n" );
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document.write( "Lets try the brute force method:<BR>\n" );
document.write( "First divide both sides by (x-2)(x-7) and we get:\r<BR>\n" );
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document.write( "3x-a=(3x^3-32x^2+81x-70)/((x-2)(x-7)) <BR>\n" );
document.write( "Next subtract 3x from both sides:\r<BR>\n" );
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document.write( "-a=(3x^3-32x^2+81x-70)/((x-2)(x-7))-3x  \r<BR>\n" );
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document.write( "Now multiply right side by ((x-2)(x-7))/((x-2)(x-7)) to get a common denominator<BR>\n" );
document.write( "-a=((3x^3-32x^2+81x-70)-3x(x-2)(x-7))/((x-2)(x-7))<BR>\n" );
document.write( "Noting that (x-2)(x-7)=x^2-9x+14 we will now expand the numerator:\r<BR>\n" );
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document.write( "-a=(3x^3-32x^2+81x-70-3x^3+27x^2-42x)/((x-2)(x-7)) collecting like terms in the numerator:\r<BR>\n" );
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document.write( "-a=(-5x^2+39x-70)/(x^2-9x+14) multiply both sides by (-1)\r<BR>\n" );
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document.write( "a=(5x^2-39x+70)/(x^2-9x+14) when we divide the quadratics, we get:\r<BR>\n" );
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document.write( "a=5+6x/(x^2-9x+14) factoring the denominator, we get\r<BR>\n" );
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document.write( "a=5+6x/((x-2)(x-7))  Where x cannot equal 2  or  7\r<BR>\n" );
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document.write( "ck<BR>\n" );
document.write( "substitute  for a in (1) and we get:\r<BR>\n" );
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document.write( "(3x-5-6x/((x-2)(x-7)))(x-2)(x-7)=3x^3-32x^2+81x-70 and<BR>\n" );
document.write( "3x(x^2-9x+14)-5(x^2-9x+14)-6x=3x^3-32x^2+81x-70 expanding left side:<BR>\n" );
document.write( "3x^3-27x^2+42x-5x^2+45x-70-6x=3x^3-32x^2+81x-70 collecting like terms on left side:\r<BR>\n" );
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document.write( "3x^3-32x^2+81x-70=3x^3-32x^2+81x-70 \r<BR>\n" );
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document.write( "Happy holidays---ptaylor\r<BR>\n" );
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