document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=288025>Question 288025</A>: <I><SPAN STYLE=\"word-break: break-all;\"> PlEASE help with polynomial long division.I've tried a million times and just cant get it. :/  (x^3+2x^2+3x-6)/(x-1) and (n^3-27)/(n-3) PlEASE show steps also =) Thanks in advance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #208753 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=208753\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Polynomial division is not much different than regular long division.\r<BR>\n" );
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document.write( "Here's how you do it step by step.\r<BR>\n" );
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document.write( "Your dividend is the expression you want to divide into.\r<BR>\n" );
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document.write( "It is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+%2B+2x%5E2+%2B+3x+-+6 ALIGN=MIDDLE  ALT=\"x%5E3+%2B+2x%5E2+%2B+3x+-+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Your divisor is the expression you want to divide into the dividend.\r<BR>\n" );
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document.write( "It is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1 ALIGN=MIDDLE  ALT=\"x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You set up your equation as shown in step 1 of the following picture.\r<BR>\n" );
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document.write( "In step 1 you are dividing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+-+x%5E2 ALIGN=MIDDLE  ALT=\"x%5E3+-+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "You subtract that from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+%2B+2x%5E2 ALIGN=MIDDLE  ALT=\"x%5E3+%2B+2x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get a remainder of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2 ALIGN=MIDDLE  ALT=\"3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "You bring down the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x ALIGN=MIDDLE  ALT=\"3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the original dividend as shown in step 1 to make the remainder equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+%2B+3x ALIGN=MIDDLE  ALT=\"3x%5E2+%2B+3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > as shown in step 2.\r<BR>\n" );
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document.write( "You divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2 ALIGN=MIDDLE  ALT=\"3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > of that remainder by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x ALIGN=MIDDLE  ALT=\"3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > which you place above the original dividend as shown in step 1.\r<BR>\n" );
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document.write( "You multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1 ALIGN=MIDDLE  ALT=\"x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x ALIGN=MIDDLE  ALT=\"3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+-+3x ALIGN=MIDDLE  ALT=\"3x%5E2+-+3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > which you subtract from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+%2B+3x ALIGN=MIDDLE  ALT=\"3x%5E2+%2B+3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > as shown in step 2.\r<BR>\n" );
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document.write( "You get a remainder of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x ALIGN=MIDDLE  ALT=\"6x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "You bring down the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the original dividend as shown in step 1 to get a remainder of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-6 ALIGN=MIDDLE  ALT=\"6x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > as shown in step 3.\r<BR>\n" );
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document.write( "You divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x ALIGN=MIDDLE  ALT=\"6x\"   DISABLED_style= \"max-width:90%; height:auto;\" > as shown in step 2 to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > which you place above <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x ALIGN=MIDDLE  ALT=\"3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the original dividend as shown in step 1.\r<BR>\n" );
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document.write( "You multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1 ALIGN=MIDDLE  ALT=\"x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > times 6 to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-6 ALIGN=MIDDLE  ALT=\"6x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > which you subtract from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-6 ALIGN=MIDDLE  ALT=\"6x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get a remainder of 0 as shown in step 4.\r<BR>\n" );
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document.write( "You stop at step 4 because you have nothing left to divide into.\r<BR>\n" );
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document.write( "Your answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+3x+%2B+6 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+3x+%2B+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > with zero remainder.\r<BR>\n" );
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document.write( "To confirm that it's good, you multiply it by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1 ALIGN=MIDDLE  ALT=\"x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get the original dividend.\r<BR>\n" );
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document.write( "That happens in steps 5 and 6 with the result shown in step 7.\r<BR>\n" );
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document.write( "Since you are able to get the same dividend that you started with, your division is good.\r<BR>\n" );
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document.write( "The result of your division is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+3x+%2B+6 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+3x+%2B+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > as shown in step 1.\r<BR>\n" );
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document.write( "Your original dividend is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+%2B+2x%5E2+%2B+3x+-+6 ALIGN=MIDDLE  ALT=\"x%5E3+%2B+2x%5E2+%2B+3x+-+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > as shown in step  and confirmed in step 7.\r<BR>\n" );
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document.write( "You are always dividing the highest order of the divider into the highest order of the remainder of the dividend.\r<BR>\n" );
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document.write( "You are then always multiplying the whole divisor by the result of that division.\r<BR>\n" );
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document.write( "You are then subtracting the result of that multiplication from the remainder.\r<BR>\n" );
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document.write( "Once you get your remainder from the division, you are always bringing down the next lower order term from the original dividend.\r<BR>\n" );
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document.write( "Follow the steps through and you'll see how it was done.\r<BR>\n" );
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document.write( "Now we'll go on to your next problem.\r<BR>\n" );
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document.write( "That problem worked out by hand is shown below:\r<BR>\n" );
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document.write( "With this problem, you are dividing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E3+-+27 ALIGN=MIDDLE  ALT=\"n%5E3+-+27\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-1 ALIGN=MIDDLE  ALT=\"n-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Since you are missing lower order exponents in the dividend, you need to fill them in.   \r<BR>\n" );
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document.write( "That will make further processing easier.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E3+-+27 ALIGN=MIDDLE  ALT=\"n%5E3+-+27\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E3+%2B+0n%5E2+%2B+0n+-+27 ALIGN=MIDDLE  ALT=\"n%5E3+%2B+0n%5E2+%2B+0n+-+27\"   DISABLED_style= \"max-width:90%; height:auto;\" > after you fill in the missing lower order exponent terms.\r<BR>\n" );
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document.write( "Now you are ready to begin.\r<BR>\n" );
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document.write( "You are always dividing the highest order of the divisor into the highest order of the remainder of the dividend.\r<BR>\n" );
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document.write( "When you start the division, the remainder of the dividend is the dividend itself.\r<BR>\n" );
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document.write( "You Divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E3 ALIGN=MIDDLE  ALT=\"n%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > as shown in step 1.\r<BR>\n" );
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document.write( "You get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2 ALIGN=MIDDLE  ALT=\"n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which you place above the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E3 ALIGN=MIDDLE  ALT=\"n%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > as shown in step 1.\r<BR>\n" );
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document.write( "You multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-3 ALIGN=MIDDLE  ALT=\"n-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2 ALIGN=MIDDLE  ALT=\"n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E3+-+3n%5E2 ALIGN=MIDDLE  ALT=\"n%5E3+-+3n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which you subtract from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E3+%2B+0n%5E2 ALIGN=MIDDLE  ALT=\"n%5E3+%2B+0n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > as shown in step 1.\r<BR>\n" );
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document.write( "You get a remainder of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3n%5E2 ALIGN=MIDDLE  ALT=\"3n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and bring down <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0n ALIGN=MIDDLE  ALT=\"0n\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the original dividend to get a remainder of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3n%5E2+%2B+0n ALIGN=MIDDLE  ALT=\"3n%5E2+%2B+0n\"   DISABLED_style= \"max-width:90%; height:auto;\" > as shown in step 2.\r<BR>\n" );
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document.write( "You divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3n%5E2 ALIGN=MIDDLE  ALT=\"3n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3n ALIGN=MIDDLE  ALT=\"3n\"   DISABLED_style= \"max-width:90%; height:auto;\" > which you place above <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0n%5E2 ALIGN=MIDDLE  ALT=\"0n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > as shown in step 1.\r<BR>\n" );
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document.write( "You multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-3 ALIGN=MIDDLE  ALT=\"n-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3n ALIGN=MIDDLE  ALT=\"3n\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3n%5E2+-+9n ALIGN=MIDDLE  ALT=\"3n%5E2+-+9n\"   DISABLED_style= \"max-width:90%; height:auto;\" > which you subtract from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3n%5E2+%2B+0n ALIGN=MIDDLE  ALT=\"3n%5E2+%2B+0n\"   DISABLED_style= \"max-width:90%; height:auto;\" > as shown in step 2.\r<BR>\n" );
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document.write( "You get a remainder of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9n ALIGN=MIDDLE  ALT=\"9n\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "You bring down the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-27 ALIGN=MIDDLE  ALT=\"-27\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the original dividend as shown in step 1.\r<BR>\n" );
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document.write( "You get a remainder of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9n-27 ALIGN=MIDDLE  ALT=\"9n-27\"   DISABLED_style= \"max-width:90%; height:auto;\" > as shown in step 3.\r<BR>\n" );
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document.write( "You divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9n ALIGN=MIDDLE  ALT=\"9n\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 9.\r<BR>\n" );
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document.write( "You place that above the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0n ALIGN=MIDDLE  ALT=\"0n\"   DISABLED_style= \"max-width:90%; height:auto;\" > as shown in step 1.\r<BR>\n" );
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document.write( "You multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-3 ALIGN=MIDDLE  ALT=\"n-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9n+-+27 ALIGN=MIDDLE  ALT=\"9n+-+27\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "You subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9n-27 ALIGN=MIDDLE  ALT=\"9n-27\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9n-27 ALIGN=MIDDLE  ALT=\"9n-27\"   DISABLED_style= \"max-width:90%; height:auto;\" > as shown in step 3 to get a remainder of 0 as shown in step 4.\r<BR>\n" );
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document.write( "Since there is nothing left to divide, you are done.\r<BR>\n" );
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document.write( "You then confirm the answer is correct by multiplying <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2+%2B+3n+%2B+9 ALIGN=MIDDLE  ALT=\"n%5E2+%2B+3n+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > as shown in step 1 by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-3 ALIGN=MIDDLE  ALT=\"n-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to see if you can get back to the original dividend.\r<BR>\n" );
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document.write( "That's done in steps 5 and 6 with the result shown in step 7.\r<BR>\n" );
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document.write( "Since you get the original dividend, the division is good.\r<BR>\n" );
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document.write( "The result of the division is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2+%2B+3n+%2B+9 ALIGN=MIDDLE  ALT=\"n%5E2+%2B+3n+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > as shown in step 1.\r<BR>\n" );
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document.write( "The original dividend is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E3+-+27 ALIGN=MIDDLE  ALT=\"n%5E3+-+27\"   DISABLED_style= \"max-width:90%; height:auto;\" > as shown above step 1 and confirmed in step 7.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );