document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=166556>Question 166556</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help me please:\r<BR>\n" );
document.write( "\n" );
document.write( "Use synthetic division to find the quotient and remainder (4x^3-6x+5)/(x-3).\r<BR>\n" );
document.write( "\n" );
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 #122755 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=122755\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (4x^3-6x+5)/(x-3).<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "this is relatively easy to do on paper but it's a real pain in the neck to type it in and have you see how it works.<BR>\n" );
document.write( "i'll do my best.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "your original equation is:<BR>\n" );
document.write( "4x^3 - 6x + 5<BR>\n" );
document.write( "you want to divide that by (x-3)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "make sure all equations are in exponential order form (highest order of exponent on the left, next highest to the right of that, next highest to the right of that, etc.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "look at your highest order exponent in  your original equation (the dividend equation).<BR>\n" );
document.write( "it is 4x^3<BR>\n" );
document.write( "what do you have to multiply (x-3) by to make the highest order of the multiplication equal to 4x^3?<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the answer is 4x^2.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you multiply (x-3) * 4x^2<BR>\n" );
document.write( "you get 4x^3 - 12x^2<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you take your original equation of 4x^3 - 6x + 5 and subtract (4x^3 - 12x^2) from it.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you get 12x^2 -6x + 5 which is the first remainder.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you look at the highest order exponent of the first remainder.<BR>\n" );
document.write( "it is 12x^2<BR>\n" );
document.write( "what do you have to multiply (x-3) by to make the highest order of the multiplication equal to 12x^2?<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the answer is 12x.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you multiply (x-3) * 12x<BR>\n" );
document.write( "you get 12x^2 - 36x<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you take the first remainder of 12x^2 - 6x + 5 and subtract (12x^2 - 36x) from it.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you get 30x + 5 which is the second remainder.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you look at the highest order exponent of the second remainder.<BR>\n" );
document.write( "it is 30x<BR>\n" );
document.write( "what do you have to multiply (x-3) by to make the highest order of the multiplication equal to 30x?<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the answer is 30.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you multiply (x-3) * 30<BR>\n" );
document.write( "you get 30x - 90<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you take the second remainder of 30x + 5 and subtract (30x - 90) from it.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you get 95 which is the third remainder.<BR>\n" );
document.write( "this is also the last remainder because there is nothing left to the right of that.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "your answer is:  4x^2 + 12x + 30 with a remainder of 95.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the 4x^2 was obtained after the first division into the original equation.<BR>\n" );
document.write( "the 12x was obtained after the second division into the first remainder.<BR>\n" );
document.write( "the 30 was obtained after the third division into the second remainder.<BR>\n" );
document.write( "the 95 is the final remainder.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "to prove your answer is correct, you multiply (4x^2 + 12x + 30) by (x-3)<BR>\n" );
document.write( "first multiply (4x^2 + 12x + 30) by -3.<BR>\n" );
document.write( "you get<BR>\n" );
document.write( "-12x^2 - 36x - 90<BR>\n" );
document.write( "then multiply (4x^2 + 12x + 30 by x.<BR>\n" );
document.write( "you get<BR>\n" );
document.write( "4x^3 + 12x^2 + 30x.<BR>\n" );
document.write( "next you add these two terms together.<BR>\n" );
document.write( "you get<BR>\n" );
document.write( "4x^3 + 12x^2 - 12x^2 + 30x - 36x - 90<BR>\n" );
document.write( "combining like terms, you get<BR>\n" );
document.write( "4x^3 - 6x - 90<BR>\n" );
document.write( "now you have to add the remainder which was 95.<BR>\n" );
document.write( "you get<BR>\n" );
document.write( "4x^3 - 6x - 90 + 95<BR>\n" );
document.write( "combining like terms, you get<BR>\n" );
document.write( "4x^3 - 6x + 5<BR>\n" );
document.write( "this is the original equation you started from so you know that the division was done properly.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );