document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1049759>Question 1049759</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help I really need to know the method for this one,but not using long division..Thank you so much:\r<BR>\n" );
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document.write( "P(x)=9x^3+12x^2+hx+k. When you divide by 3x-1, 2=remainder. When you divide by x+2, -5= remainder. Find h and k.\r<BR>\n" );
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document.write( "Please help,thank you!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #665323 by </B><A HREF=/tutors/aboutme.mpl?userid=advanced_Learner><B>advanced_Learner(501)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=advanced_Learner><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=advanced_Learner><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=665323\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> P(x)=9x^3+12x^2+hx+k. at x=1/3\r<BR>\n" );
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document.write( "2=9(1/3)^3+12(1/3)^2+h(1/3)+k.<BR>\n" );
document.write( "2=9(1/27)+12(1/9)+h(1/3)+k.<BR>\n" );
document.write( "2=(1/3)+(4/3)+(h/3)+k.<BR>\n" );
document.write( "6=(1)+(4)+(h)+3k.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2B3k ALIGN=MIDDLE  ALT=\"h%2B3k\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "at x=-2<BR>\n" );
document.write( "-5=9(-2)^3+12(-2)^2+h(-2)+k.\r<BR>\n" );
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document.write( "-5=-72+12(4)-2h+k.\r<BR>\n" );
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document.write( "-5=-72+(48)-2h+k.<BR>\n" );
document.write( "-5=(-24)-2h+k.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19 ALIGN=MIDDLE  ALT=\"19\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2h%2Bk ALIGN=MIDDLE  ALT=\"-2h%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solve<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2B3k ALIGN=MIDDLE  ALT=\"h%2B3k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19 ALIGN=MIDDLE  ALT=\"19\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2h%2Bk ALIGN=MIDDLE  ALT=\"-2h%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=linear_substitution.solver>SOLVE linear system by SUBSTITUTION</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Solve:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++1%5Ch+%2B+3%5Ck+=+1%2C%0D%0A++++-2%5Ch+%2B+1%5Ck+=+19+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++1%5Ch+%2B+3%5Ck+=+1%2C%0D%0A++++-2%5Ch+%2B+1%5Ck+=+19+%29%0D%0A++\"   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving 3*k to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ah+=+1+-+3%2Ak ALIGN=MIDDLE  ALT=\"1%2Ah+=+1+-+3%2Ak\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+1%2F1+-+3%2Ak%2F1 ALIGN=MIDDLE  ALT=\"h+=+1%2F1+-+3%2Ak%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substitute that<BR>\n" );
document.write( "  into another equation:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2A%281%2F1+-+3%2Ak%2F1%29+%2B+1%5Ck+=+19 ALIGN=MIDDLE  ALT=\"-2%2A%281%2F1+-+3%2Ak%2F1%29+%2B+1%5Ck+=+19\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that k=3. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+1%2F1+-+3%2Ak%2F1 ALIGN=MIDDLE  ALT=\"h+=+1%2F1+-+3%2Ak%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, h=-8.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+h=-8%2C+k=3+%29 ALIGN=MIDDLE  ALT=\"system%28+h=-8%2C+k=3+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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