document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1040787>Question 1040787</A>: <I><SPAN STYLE=\"word-break: break-all;\"> which of the following polynomials has a factor of x-1?.<BR>\n" );
document.write( "A) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29=x%5E3%2Bx%5E2-2x%2B1 ALIGN=MIDDLE  ALT=\"p%28x%29=x%5E3%2Bx%5E2-2x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "B) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q%28x%29=2x%5E3-x%5E2%2Bx-1 ALIGN=MIDDLE  ALT=\"q%28x%29=2x%5E3-x%5E2%2Bx-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "c) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%28x%29=3x%5E3-x-2 ALIGN=MIDDLE  ALT=\"r%28x%29=3x%5E3-x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "D) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%28x%29=-3x%5E3%2B3x%2B1 ALIGN=MIDDLE  ALT=\"s%28x%29=-3x%5E3%2B3x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #655696 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=655696\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> By the remainder theorem, if x-k is factor of p(x), then p(k) = 0.\r<BR>\n" );
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document.write( "In this case, x-k = x-1, so k = 1. Therefore, if we find a function p(x) such that p(k) = p(1) = 0 then we have found the answer.\r<BR>\n" );
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document.write( "Essentially we plug in x = 1 into each answer choice. Then we see which results in 0. \r<BR>\n" );
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document.write( "Let's go through the answer choices one by one. Starting with choice A\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29+=+x%5E3%2Bx%5E2-2x%2B1 ALIGN=MIDDLE  ALT=\"p%28x%29+=+x%5E3%2Bx%5E2-2x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%281%29+=+1%5E3%2B1%5E2-2%281%29%2B1 ALIGN=MIDDLE  ALT=\"p%281%29+=+1%5E3%2B1%5E2-2%281%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace every x with 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%281%29+=+1%2B1-2%281%29%2B1 ALIGN=MIDDLE  ALT=\"p%281%29+=+1%2B1-2%281%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%281%29+=+1%2B1-2%2B1 ALIGN=MIDDLE  ALT=\"p%281%29+=+1%2B1-2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%281%29+=+1 ALIGN=MIDDLE  ALT=\"p%281%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since the result is NOT equal to 0, this means that x-1 is NOT a factor of p(x).\r<BR>\n" );
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document.write( "Now onto choice B. Like before, plug in x = 1 to see if we get a result of 0.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q%28x%29+=+2x%5E3-x%5E2%2Bx-1 ALIGN=MIDDLE  ALT=\"q%28x%29+=+2x%5E3-x%5E2%2Bx-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q%281%29+=+2%281%29%5E3-%281%29%5E2%2B1-1 ALIGN=MIDDLE  ALT=\"q%281%29+=+2%281%29%5E3-%281%29%5E2%2B1-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace every 'x' with 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q%281%29+=+2%281%29-1%2B1-1 ALIGN=MIDDLE  ALT=\"q%281%29+=+2%281%29-1%2B1-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q%281%29+=+2-1%2B1-1 ALIGN=MIDDLE  ALT=\"q%281%29+=+2-1%2B1-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q%281%29+=+1 ALIGN=MIDDLE  ALT=\"q%281%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Again we don't get 0. So choice B is not the answer either. <BR>\n" );
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document.write( "Part C)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%28x%29+=+3x%5E3-x-2 ALIGN=MIDDLE  ALT=\"r%28x%29+=+3x%5E3-x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%281%29+=+3%281%29%5E3-1-2 ALIGN=MIDDLE  ALT=\"r%281%29+=+3%281%29%5E3-1-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in x = 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%281%29+=+3%281%29-1-2 ALIGN=MIDDLE  ALT=\"r%281%29+=+3%281%29-1-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%281%29+=+3-1-2 ALIGN=MIDDLE  ALT=\"r%281%29+=+3-1-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%281%29+=+0 ALIGN=MIDDLE  ALT=\"r%281%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We got a result of 0, so x-1 is a factor of r(x). We have our answer. Let's check part D just to complete the problem.<BR>\n" );
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document.write( "Part D)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%28x%29+=+-3x%5E3%2B3x%2B1 ALIGN=MIDDLE  ALT=\"s%28x%29+=+-3x%5E3%2B3x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%281%29+=+-3%281%29%5E3%2B3%281%29%2B1 ALIGN=MIDDLE  ALT=\"s%281%29+=+-3%281%29%5E3%2B3%281%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in x = 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%281%29+=+-3%281%29%2B3%281%29%2B1 ALIGN=MIDDLE  ALT=\"s%281%29+=+-3%281%29%2B3%281%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%281%29+=+-3%2B3%2B1 ALIGN=MIDDLE  ALT=\"s%281%29+=+-3%2B3%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%281%29+=+1 ALIGN=MIDDLE  ALT=\"s%281%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The nonzero result means x-1 is not a factor of s(x)<BR>\n" );
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document.write( "To summarize, the final answer is <font color=red>Choice C</font> </SPAN>\n" );
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