document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1029942>Question 1029942</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a polynomial function f(x) of degree 3 with real coefficients that satisfies the given conditions.\r<BR>\n" );
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document.write( "zero of 2 and zero of 4 having multiplicity 2; f(1)=-18 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #644869 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</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=644869\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Zeros are  2 and 4 and 4 again.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=k%28x-2%29%28x-4%29%5E2 ALIGN=MIDDLE  ALT=\"f%28x%29=k%28x-2%29%28x-4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which takes care of the zeros.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=k%28x-2%29%28x%5E2-8x%2B16%29 ALIGN=MIDDLE  ALT=\"f%28x%29=k%28x-2%29%28x%5E2-8x%2B16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%28x%5E3-8x%5E2%2B16x-2x%5E2%2B16x-32%29 ALIGN=MIDDLE  ALT=\"k%28x%5E3-8x%5E2%2B16x-2x%5E2%2B16x-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28k%28x%5E3-10x%5E2%2B32x-32%29%29 ALIGN=MIDDLE  ALT=\"highlight%28k%28x%5E3-10x%5E2%2B32x-32%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and then seems your choice to multiply through by k or not.\r<BR>\n" );
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document.write( "Finding k should be easier using the fully factored form.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=k%281-2%29%281-4%29%5E2=-18 ALIGN=MIDDLE  ALT=\"f%281%29=k%281-2%29%281-4%29%5E2=-18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%28-1%29%28-3%29%5E2=-18 ALIGN=MIDDLE  ALT=\"k%28-1%29%28-3%29%5E2=-18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%28-1%29%2A9=-18 ALIGN=MIDDLE  ALT=\"k%28-1%29%2A9=-18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=2 ALIGN=MIDDLE  ALT=\"k=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now you can multiply through using k=2.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28highlight%28f%28x%29=2x%5E3-20x%5E2%2B64x-64%29%29 ALIGN=MIDDLE  ALT=\"highlight%28highlight%28f%28x%29=2x%5E3-20x%5E2%2B64x-64%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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