document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1176598>Question 1176598</A>: <I><SPAN STYLE=\"word-break: break-all;\"> x−2) is a factor of 2x³+ax²+bx−2,and when this expression is divided by (x−3)the remainder is-50.<BR>\n" );
document.write( "Find a and b and the remaining factors<BR>\n" );
document.write( "a)x³-5x²-x+5,(b) x³-9x²+27x+18,(c) 2x³+x²-18x+5.State the roots of the equation 2x³+ax²+bx-2=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #803836 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=803836\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Call the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29+=+2x%5E3%2Bax%5E2%2Bbx-2 ALIGN=MIDDLE  ALT=\"p%28x%29+=+2x%5E3%2Bax%5E2%2Bbx-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "(x-2) being a factor of p(x) means that the remainder when p(x) is divided by (x-2) the remainder is 0; that means<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%282%29+=+2%282%5E3%29%2Ba%282%5E2%29%2Bb%282%29-2=0 ALIGN=MIDDLE  ALT=\"p%282%29+=+2%282%5E3%29%2Ba%282%5E2%29%2Bb%282%29-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2B4a%2B2b-2=0 ALIGN=MIDDLE  ALT=\"16%2B4a%2B2b-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4a%2B2b=-14 ALIGN=MIDDLE  ALT=\"4a%2B2b=-14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2Bb+=+-7 ALIGN=MIDDLE  ALT=\"2a%2Bb+=+-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [1]<br><BR>\n" );
document.write( "Similarly, if p(x) divided by (x-3) leaves remainder -50, that means<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%283%29+=+2%283%5E3%29%2Ba%283%5E2%29%2Bb%283%29-2+=+-50 ALIGN=MIDDLE  ALT=\"p%283%29+=+2%283%5E3%29%2Ba%283%5E2%29%2Bb%283%29-2+=+-50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=54%2B9a%2B3b-2+=+-50 ALIGN=MIDDLE  ALT=\"54%2B9a%2B3b-2+=+-50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9a%2B3b+=+-102 ALIGN=MIDDLE  ALT=\"9a%2B3b+=+-102\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a%2Bb+=+-34 ALIGN=MIDDLE  ALT=\"3a%2Bb+=+-34\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [2]<br><BR>\n" );
document.write( "Solve equations [1] and [2] to find a=-27 and b=47.<br><BR>\n" );
document.write( "The expression is 2x^3-27x^2+47x-2.<br><BR>\n" );
document.write( "We know one of the roots is 2; synthetic division leads us to<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E3-27x%5E2%2B47x-2+=+%28x-2%29%282x%5E2-23x%2B1%29 ALIGN=MIDDLE  ALT=\"2x%5E3-27x%5E2%2B47x-2+=+%28x-2%29%282x%5E2-23x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The quadratic factor has irrational roots; you can find them exactly using the quadratic formula; or you can find them approximately using a graphing calculator or similar tool.<br><BR>\n" );
document.write( "I'm guessing the a), b), and c) in your post are supposed to be the answer choices; but none of them is correct....<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );