document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=29167>Question 29167</A>: <I><SPAN STYLE=\"word-break: break-all;\"> given a polynomial and one of its factors, find the remaining factors of the polynomial.  Some factors may not be binomials.\r<BR>\n" );
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document.write( "6x^3-25x^2+2x+8;3x-2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #15945 by </B><A HREF=/tutors/aboutme.mpl?userid=Nate><B>Nate(3500)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Nate><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=15945\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your Question:<BR>\n" );
document.write( "given a polynomial and one of its factors, find the remaining factors of the polynomial.  Some factors may not be binomials.\r<BR>\n" );
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document.write( "6x^3-25x^2+2x+8;3x-2<BR>\n" );
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document.write( "My answer:\r<BR>\n" );
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document.write( "What i am going to show you is called synthetic division....\r<BR>\n" );
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document.write( "You're going to set 3x-2 to 0 to get x equaling a number<BR>\n" );
document.write( "3x-2=0 (add 2)<BR>\n" );
document.write( "3x=2   (divide by 3)<BR>\n" );
document.write( "x=2/3\r<BR>\n" );
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document.write( "Now, take the coefficients (the number in front of the variables) and set them in a side-by-side order with your x value (2/3) on the way left(if you had a 0x^2, you would still use the 0 coefficient.)\r<BR>\n" );
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document.write( "(2/3)__6__(-25)__2__8\r<BR>\n" );
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document.write( "       6                   (multiply the 2/3 and 6 and add to -25)<BR>\n" );
document.write( "           -21             (multiply the 2/3 and -21 and add to 2)<BR>\n" );
document.write( "                -12        (multiply the 2/3 and -12 and add to 8)<BR>\n" );
document.write( "                    0<BR>\n" );
document.write( "Notice that you have 6, then, -21, and last -12, so you would combine them with the degree of x is descending order and multiply by the value you were given beforehand.<BR>\n" );
document.write( "To simplify it more:<BR>\n" );
document.write( "divide by 3 to make it easier------ (6x^2-21x-12)(x-2/3)  <BR>\n" );
document.write( "3(2x^2-7x-4)(x-2/3)------     multiply by the coefficient of x^2 and the constant(the number without a variable(the number is -8)) Then, find the factors of that number (1,2,4,8,-1,-2,-4,-8). Next, find the factors that would add to equal the -7 in the equation (the answer would be -8 and 1)<BR>\n" );
document.write( "plug in the -8 and 1 to equal the -7 -------    3(2x^2-8x+x-4)(x-2/3)<BR>\n" );
document.write( "simplify                                  3{2x(x-4)+1(x-4)}(x-2/3)<BR>\n" );
document.write( "combine                                   3(2x+1)(x-4)(x-2/3)<BR>\n" );
document.write( "multiply 3 by one of the polynomials      (6x+3)(x-4)(x-2/3)\r<BR>\n" );
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document.write( "(6x+3)(x-4)(x-2/3) is your answer!\r<BR>\n" );
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document.write( " </SPAN>\n" );
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