document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=583689>Question 583689</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help me solve this? <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816x%5E5+-+32x%5E4+-+81x+%2B+162%29+%2F+%28x+-+2%29 ALIGN=MIDDLE  ALT=\"%2816x%5E5+-+32x%5E4+-+81x+%2B+162%29+%2F+%28x+-+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > I am supposed to solve and state whether the binomial is a factor of the polynomial.\r<BR>\n" );
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document.write( "I used synthetic division to drop the coefficients and got: \r<BR>\n" );
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document.write( "2] 16 -32 0 0 -81   162<BR>\n" );
document.write( "    0  32 0 0   0  -162<BR>\n" );
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document.write( "    16  0 0 0 0 -81  0<BR>\n" );
document.write( "(The zeroes in the top row are because there are no x-cubed and x-squared variables, therefore they're respresented by a zero, right?)\r<BR>\n" );
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document.write( "Multiple choice allowed me the answers of: <BR>\n" );
document.write( "A - 1348; no<BR>\n" );
document.write( "B - 0; yes<BR>\n" );
document.write( "C - 700; yes<BR>\n" );
document.write( "D - 0; no\r<BR>\n" );
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document.write( " I am pretty sure the answer is C because my remainder is zero, and x-2 is a factor of the original equation. If this is not right, can you please show me what I've done wrong?<BR>\n" );
document.write( "(Also, I apologize if the synthetic division does not line up properly when submitted and if it makes it harder for you to read.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #372537 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=372537\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "No.  Not answer C.\r<BR>\n" );
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document.write( "The numeric part of the answer is supposed to be the remainder that results from the synthetic division which is the same as the value of the function evaluated at the divisor.  That is, if your function is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(x)\"> and the synthetic division divisor is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\"> because you are testing <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ -\ a\"> as a factor of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(x)\">, then the rightmost number in the third row of numbers in your synthetic division is equal to <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(a)\">.  And since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ -\ a\"> is a factor of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(x)\"> if and only if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(a)\ =\ 0\">, your rightmost result is, in fact, 0, that means B is your answer.  Answers C and D are impossible because, in the case of C, the number cannot be non-zero and the answer yes, and in the case of D, the number cannot be zero and the answer no.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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