document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1051087>Question 1051087</A>: <I><SPAN STYLE=\"word-break: break-all;\"> PLEASE HELP!!!!\r<BR>\n" );
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document.write( "use synthetic division and the Factor <BR>\n" );
document.write( "Theorem to determine whether the given binomial is a <BR>\n" );
document.write( "factor of P(x).\r<BR>\n" );
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document.write( "P(x)=x^3+2x^2-5x-6, x-2\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #666690 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=666690\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> change the sign of the -2 to 2 and divide\r<BR>\n" );
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document.write( "2/1===+2====-5====-6<BR>\n" );
document.write( "==1=(2)=4=(8)=3==(6)0, the parentheses are the intermediate products which are added to the coefficients. You multiply each result by +2 and add.<BR>\n" );
document.write( "Because the remainder is 0, it factored.<BR>\n" );
document.write( "What is left is a 1===4====3<BR>\n" );
document.write( "These are coefficients of a polynomial to one less power, here x^2+4x+3<BR>\n" );
document.write( "That happens to factor as well (x+3)(x+1), but that isn't required to be answered here.  The polynomial factors completely, and x-2 is a factor, and x=2 is the root.<BR>\n" );
document.write( "How do you remember whether to change the sign?<BR>\n" );
document.write( "Use a polynomial you know, like x^2-6x+9 where the factors are (x-3)^2<BR>\n" );
document.write( "The roots are x=3<BR>\n" );
document.write( "If you use 3, you get a remainder of 0. </SPAN>\n" );
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