document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=970032>Question 970032</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help!! I don't know what I am doing!!\r<BR>\n" );
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document.write( "Use the remainder theorem to find the remainder when f(x) is divided by x+4. Then use the factor theorem to determine whether x+4 is a factor of f(x).<BR>\n" );
document.write( "f(x)=4x^6-64x^4+x^2-18\r<BR>\n" );
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document.write( "Thank you 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 #592797 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</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=592797\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This mostly means the use of synthetic division to check if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a root of f(x).  Either remainder is zero or it is nonzero.  The dividend to use in the division must be  according to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=4x%5E6%2B0x%5E5-64x%5E4%2B0x%5E3%2Bx%5E2%2B0%2Ax-18 ALIGN=MIDDLE  ALT=\"f%28x%29=4x%5E6%2B0x%5E5-64x%5E4%2B0x%5E3%2Bx%5E2%2B0%2Ax-18\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "In case you are not yet comfortable with synthetic division, you can use polynomial division and the divisor will be x+4.\r<BR>\n" );
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document.write( "(Not showing the synthetic division steps or process)\r<BR>\n" );
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document.write( "---<BR>\n" );
document.write( "Trying to clear confusion:<BR>\n" );
document.write( "Polynomial division works the same way as regular Long Division;<BR>\n" );
document.write( "Account must be made for ALL terms of the powers of x, whether shown in the function or not; if not present in the function, then their coefficients are 0.<BR>\n" );
document.write( "Remainder of zero means the value tested IS a root of the function;<BR>\n" );
document.write( "<s>Remainder being non-zero means that the remainder is the value of the function at that quantity used as the \"divisor\" in synthetic division.  In other words, the possible root tested gives a remainder which is the value of the function at that possible root tested.</s>\r<BR>\n" );
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document.write( "The actual Remainder Theorem and Factor Theorem express that better.  This is in your College Algebra/Pre-Calculus textbook.\r<BR>\n" );
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document.write( "----\r<BR>\n" );
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document.write( "The table of processing data for synthetic division:\r<BR>\n" );
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document.write( "_______-4_____|______4_____0_____-64_____0_____1_____0_____-18<BR>\n" );
document.write( "______________|<BR>\n" );
document.write( "______________|___________-16_____64______0_____0____-4_____16<BR>\n" );
document.write( "______________|____________________________________________________<BR>\n" );
document.write( "____________________4_____-16_____0_____0______1_____-4_____<b>-2</b>\r<BR>\n" );
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document.write( "The result for this specific example:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28highlight%28f%28-4%29=-2%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28highlight%28f%28-4%29=-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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