document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=175363>Question 175363</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2x^3 - 5x^2 + 22x + 51/2x + 3\r<BR>\n" );
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document.write( "answer: x^2 -4x +17\r<BR>\n" );
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document.write( "need a break down of how my text book got that answer i know how they got x^2 and +17 not sure how they got the -4X\r<BR>\n" );
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document.write( "please break down answer in long division form radther then synthetic division  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #130421 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=130421\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> here's how i did it and the answer i got.<BR>\n" );
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document.write( "problem:<BR>\n" );
document.write( "(2x^3 - 5x^2 + 22x + 51) divided by (2x + 3)<BR>\n" );
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document.write( "first part of quotient is x^2 because 2x * x^2 = 2x^3<BR>\n" );
document.write( "x^2 * (2x+3) = (2x^3 + 3x^2)<BR>\n" );
document.write( "first remainder is (2x^3 - 5x^2 + 22x + 51) minus (2x^3 + 3x^2) = (-8x^2 + 22x + 51)<BR>\n" );
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document.write( "second part of quotient is -4x because -4x * 2x = -8x^2<BR>\n" );
document.write( "-4x * (2x+3) = (-8x^2 - 12x)<BR>\n" );
document.write( "second remainder is (-8x^2 + 22x + 51) minus (-8x^2 - 12x) = (34x + 51)<BR>\n" );
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document.write( "third part of quotient is 17 because 17 * 2x = 34x<BR>\n" );
document.write( "17 * (2x+3) = (34x + 51)<BR>\n" );
document.write( "third remainder is (34x + 51) minus (34x + 51) = 0<BR>\n" );
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document.write( "the answer is:<BR>\n" );
document.write( "(x^2 - 4x + 17)<BR>\n" );
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document.write( "to prove, multiply (2x+3) * (x^2-4x+17) and you should get back to the original equation.<BR>\n" );
document.write( "multiplying out, we get:<BR>\n" );
document.write( "2x^3 -8x^2 + 34x + 3x^2 - 12x + 51<BR>\n" );
document.write( "combining like terms, we get:<BR>\n" );
document.write( "2x^3 -5x^2 + 22x + 51<BR>\n" );
document.write( "this is the original equation so we're good.<BR>\n" );
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document.write( "your question:<BR>\n" );
document.write( "how did they get the -4x?<BR>\n" );
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document.write( "1. you always divide the highest order of the divisor into the highest order of the dividend.<BR>\n" );
document.write( "2. you then multiply the result of that division by the whole divisor.<BR>\n" );
document.write( "3. you then subtract the result of that multiplication from the dividend to get the remainder which becomes the new dividend<BR>\n" );
document.write( "4. you continue the first 3 steps until the highest order of the dividend is less than the highest order of the divisor.  take that over the divisor and you have your final remainder.<BR>\n" );
document.write( "in this problem, your final remainder was 0 / (2x+3) which became 0 which meant you had no remainder.<BR>\n" );
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document.write( "the highest order of the divisor was 2x<BR>\n" );
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document.write( "the first time the dividend was the original equation so we divided 2x into the highest order of the dividend which was x^3 to get x^2<BR>\n" );
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document.write( "the second time the dividend was the first remainder so we divided 2x into the highest order of the dividend which was -8x^2 to get -4x.<BR>\n" );
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document.write( "the third time the dividend was the second remainder so we divided 2x into the highest order of the dividend which was 34x to get 17.<BR>\n" );
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document.write( "hope that helps.<BR>\n" );
document.write( "let me know if you're still unsure how they got the -4x.<BR>\n" );
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