document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=38302>Question 38302</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Divide\r<BR>\n" );
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document.write( "A. Use long division to divide x³+6x²-x-30 by x²+8x+15\r<BR>\n" );
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document.write( "B. Use synthetic division to divide (x³+5x²-18)/(x+3) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #23795 by </B><A HREF=/tutors/aboutme.mpl?userid=junior403><B>junior403(76)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=junior403><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=23795\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A. Use long division to divide x³+6x²-x-30 by x²+8x+15<BR>\n" );
document.write( "We set up a long division problem like this...<BR>\n" );
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document.write( "x^2+8x+15)X^3+6x^2-x-30<BR>\n" );
document.write( "We can now start with the first variable (X^2)and find the value that will make the divisor (x^3) true. (x^2 * x = x^3)<BR>\n" );
document.write( "Then multiply that answer by the remaining variables. (x * 8x = 8x^2) and (x * 15 = 15x) Then we distribute a negative to subtract that line from the top line to get a new set of numbers...and repeat.<BR>\n" );
document.write( "x^2 multiplied by what makes -2x^2, and so on just like long division w/real numbers...<BR>\n" );
document.write( "So...<BR>\n" );
document.write( "_______________x_-_2_______<BR>\n" );
document.write( "x^2+8x+15)x^3+6x^2 - x -30<BR>\n" );
document.write( "________-(x^3+8x^2+15x) <BR>\n" );
document.write( "_____________-2x^2-16x -30<BR>\n" );
document.write( "____________+2X^2+16X +30<BR>\n" );
document.write( "_______________________0\r<BR>\n" );
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document.write( "The answer is x-2.<BR>\n" );
document.write( "To check, simply multiply x^2+8x+15(x-2) = x^3+6x^2-x-30<BR>\n" );
document.write( "Its kind of hard to show all the work here, but I hope you get the idea.<BR>\n" );
document.write( "B. Use synthetic division to divide (x³+5x²-18)/(x+3)<BR>\n" );
document.write( "This process can be a little tricky.<BR>\n" );
document.write( "First we change the x+3 into x-(-3)<BR>\n" );
document.write( "Now just write the coefficients of x^3 5x^2 18 with -3 on the left<BR>\n" );
document.write( "-3)1  5  18 (set up like long division)<BR>\n" );
document.write( "First carry down the 1 by itself.<BR>\n" );
document.write( "-3)1  5  18 <BR>\n" );
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document.write( "Then multiply -3(1) and place the answer under the second column.<BR>\n" );
document.write( "-3)1  5  18 <BR>\n" );
document.write( "___-3____<BR>\n" );
document.write( "__1<BR>\n" );
document.write( "Then subtract...<BR>\n" );
document.write( "-3)1  5  18 <BR>\n" );
document.write( "___-3____<BR>\n" );
document.write( "__1_2<BR>\n" );
document.write( "then multiply the -3 by that result...<BR>\n" );
document.write( "-3)1  5  18 <BR>\n" );
document.write( "___-3-6<BR>\n" );
document.write( "__1_2<BR>\n" );
document.write( "And subtract...<BR>\n" );
document.write( "-3)1  5  18 <BR>\n" );
document.write( "___-3-6<BR>\n" );
document.write( "__1_2_12 (12 is the remainder, so it is written over the divisor x+3)<BR>\n" );
document.write( "Now the result 1 2 12 can take the original signs...<BR>\n" );
document.write( "1x + 2 -12/x+3<BR>\n" );
document.write( "And this is the final answer...<BR>\n" );
document.write( "I hope this helps.<BR>\n" );
document.write( "Let me know if you have any further questions about this.<BR>\n" );
document.write( "Thanks.<BR>\n" );
document.write( "Good Luck!\r<BR>\n" );
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document.write( "Good Luck! </SPAN>\n" );
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