document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=477248>Question 477248</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me to solve those problems. I would really appreciate any help.Thanks!<BR>\n" );
document.write( "1)There is a polynomial which, when multiplied by x^2+2x+3, gives 2x^5+3x^4+8x^3+8x^2+18x+9. What is that polynomial?<BR>\n" );
document.write( "2)What are the coordinates of the points where the graphs of f(x) = x^3-x^2 + x + 1 and g(x) = x^3 + x^2 + x-1 intersect?<BR>\n" );
document.write( "3)The polynomial f(x) has degree 2. If f(0) =-21, f(1) = -16, and f(2) = -9, then what are the x-intercepts of the graph of f? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #327177 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=327177\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) Carry out long division of polynomial. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28+2x%5E5%2B3x%5E4%2B8x%5E3%2B8x%5E2%2B18x%2B9%29%2F%28x%5E2%2B2x%2B3%29+=+2x%5E3+-+x%5E2+%2B+4x+%2B+3 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2)  Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+-+x%5E2+%2B+x+%2B+1+=+x%5E3+%2B+x%5E2+%2B+x+-+1 ALIGN=MIDDLE  ALT=\"x%5E3+-+x%5E2+%2B+x+%2B+1+=+x%5E3+%2B+x%5E2+%2B+x+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+=+2 ALIGN=MIDDLE  ALT=\"2x%5E2+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+1 ALIGN=MIDDLE  ALT=\"x%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ==> x = -1, 1<BR>\n" );
document.write( "When x = -1, f(-1) = g(-1) = -2<BR>\n" );
document.write( "When x = 1, f(1) = g(1) = 2<BR>\n" );
document.write( "==> points of intersection are (-1,-2) and (1,2).\r<BR>\n" );
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document.write( "3) let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"f%28x%29+=+ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "f(0) = -21 ==> c = -21.<BR>\n" );
document.write( "f(1) = -16 ==> a + b - 21 = -16 ==> a+b = 5<BR>\n" );
document.write( "f(-1) = -9 ==> 4a + 2b - 21 = -9 ==> 4a + 2b = 12 <==> 2a + b = 6.<BR>\n" );
document.write( "Subtract the top equation from the bottom equation, to get a = 1<BR>\n" );
document.write( "==> b = 4.<BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+x%5E2+%2B+4x+-21+=+%28x%2B7%29%28x-3%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+x%5E2+%2B+4x+-21+=+%28x%2B7%29%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "==> x-intercepts are (-7, 0) and (3,0). </SPAN>\n" );
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