document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1073398>Question 1073398</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone please explain why choice D is correct and why choices A, B, C are incorrect?\r<BR>\n" );
document.write( "\n" );
document.write( "For a polynomial p(x), the value of p(3) is &#8722;2. Which of the following must be true about p(x) ?\r<BR>\n" );
document.write( "\n" );
document.write( "A) x&#8722;5 is a factor of p(x).<BR>\n" );
document.write( "B) x&#8722;2 is a factor of p(x).<BR>\n" );
document.write( "C) x+2 is a factor of p(x).<BR>\n" );
document.write( "D) The remainder when p(x) is divided by x&#8722;3 is &#8722;2. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #688222 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52788)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=688222\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "The statement D) is true. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The reference: The remainder theorem.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<U>Theorem</U> &nbsp;&nbsp;(<U><I>the remainder theorem</I></U>)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "&nbsp;&nbsp; <B>1</B>. The remainder of division the polynomial &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp; by the binomial &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-a ALIGN=MIDDLE  ALT=\"x-a\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp; is equal to the value &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28a%29 ALIGN=MIDDLE  ALT=\"f%28a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp; of the polynomial. \r\n" );
document.write( "\r\n" );
document.write( "&nbsp;&nbsp; <B>2</B>. The binomial &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-a ALIGN=MIDDLE  ALT=\"x-a\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp; divides the polynomial &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp; if and only if the value of &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp; is the root of the polynomial &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, &nbsp;i.e. &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28a%29+=+0 ALIGN=MIDDLE  ALT=\"f%28a%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r\n" );
document.write( "\r\n" );
document.write( "&nbsp;&nbsp; <B>3</B>. The binomial &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-a ALIGN=MIDDLE  ALT=\"x-a\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp; factors the polynomial &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp; if and only if the value of &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp; is the root of the polynomial &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, &nbsp;i.e. &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28a%29+=+0 ALIGN=MIDDLE  ALT=\"f%28a%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "\n" );
document.write( "See the lesson \r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Divisibility-of-polynomial-f%28x%29-by-binomial-x-a.lesson>Divisibility of polynomial f(x) by binomial x-a</A>\r<BR>\n" );
document.write( "\n" );
document.write( "in this site.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This lesson is the part of the (free of charge) online textbook in ALGEBRA-I in this site\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "under the topic \"<U>Divisibility of polynomial f(x) by binomial (x-a). The Remainder theorem</U>\".\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );