document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=188390>Question 188390</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the zeroes of f(x) = x^4-x^3-4x^2+4x.\r<BR>\n" );
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document.write( "thanks in advance </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #141231 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=141231\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the zeroes of f(x) = x^4-x^3-4x^2+4x<BR>\n" );
document.write( "x^4-x^3-4x^2+4x = 0<BR>\n" );
document.write( "Factor:<BR>\n" );
document.write( "x(x^3-x^2-4x+4) = 0<BR>\n" );
document.write( "x = 0 is one of the zeroes.<BR>\n" );
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document.write( "Since the coefficients of x^3-x^2-4x+4 add up zero, x=1 is a zero.<BR>\n" );
document.write( "Use synthetic division to find the other zeroes:<BR>\n" );
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document.write( "1)....1....-1....-4....4<BR>\n" );
document.write( ".......1.....0.....-4..|..0\r<BR>\n" );
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document.write( "The remaining factor is x^2-4 which<BR>\n" );
document.write( "factors as (x-2)(x+2).<BR>\n" );
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document.write( "So, the four zeroes are x= 0 or x=1 or x = 2 or x=-2<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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