document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=280473>Question 280473</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In figuring out a Polynomial Long division problem. How do you know when the number is a + or a -, and how do you figure out when you need to add or subtract. \r<BR>\n" );
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document.write( "12x^3-14x^2+11x-20 / 3x-5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #203878 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=203878\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You may reference the following picture:\r<BR>\n" );
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document.write( "Equation you want to divide is equal to:\r<BR>\n" );
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document.write( "12x^3 - 14x^2 + 11x - 20\r<BR>\n" );
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document.write( "you are dividing this by:\r<BR>\n" );
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document.write( "3x-5\r<BR>\n" );
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document.write( "This is very similar to regular long division with some minor adjustmenjts.\r<BR>\n" );
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document.write( "First you divide the highest order of the divisor into the highest order of the dividend.\r<BR>\n" );
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document.write( "It helps to order both your equations in order of their exponents with the highest exponent first followed by the next highest, etc.\r<BR>\n" );
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document.write( "Your equations are already in this order.\r<BR>\n" );
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document.write( "Divide 3x into 12x^3\r<BR>\n" );
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document.write( "It goes 4x^2 times because 3x * 4x^2 = 12x^3\r<BR>\n" );
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document.write( "Put 4x^2 on top and then multiply (3x-5) by 4x^2 and put the result of that under the appropriate ordered term of the dividend.\r<BR>\n" );
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document.write( "In this case, the result is 12x^3 -20x^2 and you place it underneath as shown.\r<BR>\n" );
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document.write( "Then you SUBTRACT 12x^3 - 20x^2 from 12x^3 - 14x^2.\r<BR>\n" );
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document.write( "-14x^2 - (-20x^2) = -14x^2 + 20x^2 = 6x^2.\r<BR>\n" );
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document.write( "You are subtracting, but you have to be careful of the signs.\r<BR>\n" );
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document.write( "When you subtract a minus, it's the same as adding a plus.<BR>\n" );
document.write( "When you add a minus, it's the same as subtracting a plus.\r<BR>\n" );
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document.write( "You started off with -14x^2.\r<BR>\n" );
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document.write( "You subtracted a -20x^2.\r<BR>\n" );
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document.write( "That's the same as adding a +20x^2\r<BR>\n" );
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document.write( "-14x^2 + 20x^2 = 6x^2.\r<BR>\n" );
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document.write( "You are always subtracting, but you have to be careful of the signs.   \r<BR>\n" );
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document.write( "Anyway, you bring down the result to get 6x^2 and then you add the next lower order term to it.   \r<BR>\n" );
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document.write( "That gets you 6x^2 + 11x as shown.\r<BR>\n" );
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document.write( "You divide 3x into 6x^2 to get 2x.\r<BR>\n" );
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document.write( "You put that on top so now you have 4x^2 + 2x.\r<BR>\n" );
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document.write( "You multiply 3x-5 by 2x to get 6x^2 - 10x.\r<BR>\n" );
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document.write( "Now you subtract 6x^2 - 10x from 6x^2 + 11x.\r<BR>\n" );
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document.write( "11x minus -10x is the same as 11x plus 10x and that equals 21x.\r<BR>\n" );
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document.write( "When you subtract a minus, it's the same as adding a plus.\r<BR>\n" );
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document.write( "6x^2 - 6x^2 = 0.\r<BR>\n" );
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document.write( "You bring down the next lower order term and you have 21x - 20\r<BR>\n" );
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document.write( "You divide 3x into 21x to get 7.\r<BR>\n" );
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document.write( "You multiply 7 times 3x-5 to get 21x - 35.\r<BR>\n" );
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document.write( "You subtract 21x - 35 from 21x - 20 to get 15\r<BR>\n" );
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document.write( "-20 minus -35 is the same as -20 plus 35 and the result is 15.\r<BR>\n" );
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document.write( "Once again you are subtracting a minus which is equivalent to adding a plus.\r<BR>\n" );
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document.write( "You confirm your answer is correct by multiplying the result with the divisor as shown in the picture.\r<BR>\n" );
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document.write( "ADDITIONAL INFORMATION\r<BR>\n" );
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document.write( "By bringing down the next lower order term, I mean the next lower order term that SHOULD be there, but might not necessarily be there.\r<BR>\n" );
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document.write( "You avoid this problem by rewriting your divident is the next lower order term is not there.\r<BR>\n" );
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document.write( "Example:\r<BR>\n" );
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document.write( "Divide 3x-5 into 15x^5 + 32\r<BR>\n" );
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document.write( "The next lower order term is x^4 which is not there, then x^3 which is not there, then x^2 which is not there, then x which is not there.\r<BR>\n" );
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document.write( "You write your dividend as follows:\r<BR>\n" );
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document.write( "5x^5 + 32 = 15x^5 + 0x^4 + 0x^3 + 0x^2 + 0x + 35\r<BR>\n" );
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document.write( "Now the next lower order terms are all there and you can avoid possible confusion further down.\r<BR>\n" );
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document.write( "Your first confusion would have been when you divided 3x into 15x^5 to get 5x^4\r<BR>\n" );
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document.write( "Then you would multiply 5x^4 by 3x-5 to get 15x^5 - 25x^4\r<BR>\n" );
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document.write( "Now you want to subtract 15x^5 - 25x^4 from 15x^5 + 0x^4.\r<BR>\n" );
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document.write( "If  you did not put that 0x^4 in the dividend to start with, you would have been confused and everything would have been all out of place.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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