document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=31083>Question 31083</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please, I need help with this problem:<BR>\n" );
document.write( "Assume that (X-2) is a factor of the polynomial f(x)=x^3+a(x^2)+bx+2 and that f(x) gives a remainder of -3 when it is divided by x+1. Then, a=?, b=?.\r<BR>\n" );
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document.write( "What I did is I used the factor they gave me and used the 2 as a root. It gave me 4a+2b=-10 and so I planned to use and solve a system of equations with what I could get from the other information they give me with the problem. I'm stuck though, cause I have no idea of what to do with the remainder data...\r<BR>\n" );
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document.write( "Please help, and thanks so much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #18072 by </B><A HREF=/tutors/aboutme.mpl?userid=mukhopadhyay><B>mukhopadhyay(490)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mukhopadhyay><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=18072\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x)=x^3+a(x^2)+bx+2 <BR>\n" );
document.write( "Since (x-2) is a factor, f(2) should be zero<BR>\n" );
document.write( "f(2)=2^3+a(2^2)+2b+2=0<BR>\n" );
document.write( "=>8 + 4a + 2b + 2=0<BR>\n" );
document.write( "=>4a + 2b + 10 = 0<BR>\n" );
document.write( "=>2(2a + b + 5) = 0<BR>\n" );
document.write( "=>2a + b = -5\r<BR>\n" );
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document.write( "When divided by (x+1), the remainder is -3<BR>\n" );
document.write( "=>f(-1)=-3<BR>\n" );
document.write( "=>(-1)^3 + a(-1)^2 + 2b + 2 = -3<BR>\n" );
document.write( "=>-1 + a + 2b + 2 = -3<BR>\n" );
document.write( "=>a + 2b + 1 = -3<BR>\n" );
document.write( "=>a + 2b = -4\r<BR>\n" );
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document.write( "2a + b = -5 =>b = -5 - 2a<BR>\n" );
document.write( "Substituting b in the other equation a + 2b = -4 gives<BR>\n" );
document.write( "a + 2(-5 - 2a) = -4<BR>\n" );
document.write( "=>a - 4a = 6<BR>\n" );
document.write( "=>-3a=6<BR>\n" );
document.write( "=>a=-2\r<BR>\n" );
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document.write( "So, b = -5 - 2(-2) = -1\r<BR>\n" );
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document.write( "Answer: a=-2 and b=-1\r<BR>\n" );
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document.write( " </SPAN>\n" );
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