document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=925084>Question 925084</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Factor f(x)=3x^4-54x^2+96x-45, given that 1 is a zero of f with multiplicity 2. (Use either polynomial long division or synthetic division.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #561314 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=561314\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%5E2=x%5E2-2x%2B1 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2=x%5E2-2x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  the square because multiplicity 2.\r<BR>\n" );
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document.write( "Perform the division, polynomial division.  You must include the term for x^3 in the dividend.\r<BR>\n" );
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document.write( "_________________|________3x^2__+6x____-45__________________Quotient Line<BR>\n" );
document.write( "______________________________________________<BR>\n" );
document.write( "x^2-2x+1_________|________3x^4+0*x^3-54x^2+96x-45<BR>\n" );
document.write( "__________________________3x^4-6x^3+ 3x^2<BR>\n" );
document.write( "_____________________________0+6x^3-57x^2+96x<BR>\n" );
document.write( "_______________________________6x^3-12x^2+6x<BR>\n" );
document.write( "________________________________0__-45x^2+90x-45<BR>\n" );
document.write( "___________________________________-45x^2+90x-45<BR>\n" );
document.write( "_________________________________________________<BR>\n" );
document.write( "__________________________________________0+0+0_________Remainder 0\r<BR>\n" );
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document.write( "The quotient has a scalar factor, so although factoring not yet complete, you know you have  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%5E2%2A3%2A%28x%5E2%2B2x-15%29 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2%2A3%2A%28x%5E2%2B2x-15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >; which you can finish into<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%283%28x-1%29%5E2%28x-3%29%28x%2B5%29%29 ALIGN=MIDDLE  ALT=\"highlight%283%28x-1%29%5E2%28x-3%29%28x%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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