document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=166602>Question 166602</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with the following:\r<BR>\n" );
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document.write( "Use long division to find the quotient Q(x) and the remainder R(x) when P(x) is divided by d(x).\r<BR>\n" );
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document.write( "P(x)=x^4+2x^3-2x+4<BR>\n" );
document.write( "d(x)=x-2\r<BR>\n" );
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document.write( "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 #122790 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=122790\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> here's how it's done.<BR>\n" );
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document.write( "you want to divide (x^4 + 2x^3 - 2x + 4) by (x-2).<BR>\n" );
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document.write( "first you make sure your equation and your divisor are in the correct exponential order (highest exponent first, then next lower, then next lower, etc.)<BR>\n" );
document.write( "they are that way already.<BR>\n" );
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document.write( "next you divide the highest order of your divisor into the highest order of the equation to be divided which is the original equation.<BR>\n" );
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document.write( "that would be (x^4) divided by (x) which equals (x^3).<BR>\n" );
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document.write( "you multiply (x-2) * (x^3) to get (x^4 - 2x^3).<BR>\n" );
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document.write( "you subtract that from your original equation.<BR>\n" );
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document.write( "(x^4 + 2x^3 - 2x + 4) - (x^4 - 2x^3) is the same as<BR>\n" );
document.write( "(x^4 + 2x^3 - 2x + 4)- (x^4) + (2x^3).<BR>\n" );
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document.write( "your first remainder is: (4x^3 - 2x + 4).<BR>\n" );
document.write( "the first term in your answer is (x^3).<BR>\n" );
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document.write( "next you divide the highest order of your divisor into the highest order of the equation to be divided which would be your first remainder.<BR>\n" );
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document.write( "that would be (4x^3) divided by (x) which equals (4x^2).<BR>\n" );
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document.write( "you multiply (x-2) * (4x^2) to get (4x^3 - 8x^2)<BR>\n" );
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document.write( "you subtract that from your first remainder.<BR>\n" );
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document.write( "(4x^3 - 2x + 4) - (4x^3 - 8x^2) is the same as<BR>\n" );
document.write( "(4x^3 - 2x + 4) - (4x^3) + (8x^2).<BR>\n" );
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document.write( "your second remainder is (8x^2 - 2x + 4).<BR>\n" );
document.write( "the second term in your answer is (4x^2).<BR>\n" );
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document.write( "next you divide the highest order of your divisor into the highest order of the equation to be divided which would be your second remainder.<BR>\n" );
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document.write( "that would be (8x^2) divided by (x) which equals (8x).<BR>\n" );
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document.write( "you multiply (x-2) * (8x) to get (8x^2 - 16x).<BR>\n" );
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document.write( "you subtract that from your second remainder.<BR>\n" );
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document.write( "(8x^2 - 2x + 4) - (8x^2 - 16x) is the same as<BR>\n" );
document.write( "(8x^2 - 2x + 4) - (8x^2) + (16x).<BR>\n" );
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document.write( "your third remainder is (14x + 4).<BR>\n" );
document.write( "the third term in your answer is (8x).<BR>\n" );
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document.write( "next you divide the highest order of your divisor into the highest order of the equation to be divided which would be your third remainder.<BR>\n" );
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document.write( "that would be (14x) divided by (x) which equals (14).<BR>\n" );
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document.write( "you multiply (x-2) * (14) to get (14x - 28).<BR>\n" );
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document.write( "you subtract that from your third remainder.<BR>\n" );
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document.write( "(14x + 4) - (14x - 28) is the same as<BR>\n" );
document.write( "(14x + 4) - (14x) + (28).<BR>\n" );
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document.write( "your fourth remainder is (32).<BR>\n" );
document.write( "the fourth term in your answer is (14).<BR>\n" );
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document.write( "since the highest order of your equation to be divided is less then the highest order of the equation to be divided, you are done.<BR>\n" );
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document.write( "your fourth remainder is your final remainder making it the remainder of the division.<BR>\n" );
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document.write( "you add up all the terms in your answer to get:<BR>\n" );
document.write( "(x^3 + 4x^2 + 8x + 14) + 32.<BR>\n" );
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document.write( "in order to prove your answer is correct, you multiply this answer by (x-2) and you should get back to your original equation after adding in the remainder.<BR>\n" );
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document.write( "(x-2) * (x^3 + 4x^2 + 8x + 14) are the factors to be multiplied.<BR>\n" );
document.write( "first you multiply all terms of the equation by (x).<BR>\n" );
document.write( "you get:<BR>\n" );
document.write( "(x^4 + 4x^3 + 8x^2 + 14x) equals first part of multiplication.<BR>\n" );
document.write( "then you multiply all terms of the equation by (-2).<BR>\n" );
document.write( "you get:<BR>\n" );
document.write( "(-2x^3 -8x^2 -16x -28) equals second part of multiplication.<BR>\n" );
document.write( "you add the first part and the second part of your multiplication together to get.<BR>\n" );
document.write( "(x^4 + 4x^3 - 2x^3 + 8x^2 - 8x^2 + 14x - 16x - 28) which becomes<BR>\n" );
document.write( "(x^4 + 2x^3 - 2x - 28)<BR>\n" );
document.write( "you add the remainder of 32 to this to make it:<BR>\n" );
document.write( "(x^4 + 2x^3 - 2x + 4).<BR>\n" );
document.write( "since this the original equation you started with, your division is good.<BR>\n" );
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document.write( " </SPAN>\n" );
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