document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=159653>Question 159653</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Pls , help me to solve this problem\"<BR>\n" );
document.write( "(2x^3+x^2)-(8x-4)=0<BR>\n" );
document.write( "Thanks<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #117807 by </B><A HREF=/tutors/aboutme.mpl?userid=midwood_trail><B>midwood_trail(310)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=midwood_trail><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=117807\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (2x^3+x^2)-(8x-4)= 0\r<BR>\n" );
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document.write( "The first thing you want to do is remove the parentheses.\r<BR>\n" );
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document.write( "Do you see the negative sign in front of the quantity -(8x-4)?\r<BR>\n" );
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document.write( "Believe it or not, there is an invisible -1 there.  You must multiply -1 by every term inside the parentheses.\r<BR>\n" );
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document.write( "So, let's do that first.\r<BR>\n" );
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document.write( "-1 times 8x = -8x\r<BR>\n" );
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document.write( "-1 times -4 = 4\r<BR>\n" );
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document.write( "We no have this equation:\r<BR>\n" );
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document.write( "2x^3+x^2 -8x + 4 = 0\r<BR>\n" );
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document.write( "We make two groups here:\r<BR>\n" );
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document.write( "2x^3+x^2...GROUP A\r<BR>\n" );
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document.write( "-8x + 4...Group B\r<BR>\n" );
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document.write( "We factor each group separately.\r<BR>\n" );
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document.write( "2x^3+x^2 becomes x^2(2x + 1)\r<BR>\n" );
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document.write( "-8x + 4 becomes -4(2x - 1)\r<BR>\n" );
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document.write( "We now have three factors:\r<BR>\n" );
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document.write( "(x^2 - 4), (2x + 1) and (2x - 1)\r<BR>\n" );
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document.write( "We equate each factor to zero and solve for x.\r<BR>\n" );
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document.write( "x^2 - 4 = 0\r<BR>\n" );
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document.write( "x^2 = 4\r<BR>\n" );
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document.write( "We take square root of both sides and get x = -2 and x = 2\r<BR>\n" );
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document.write( "2x + 1 = 0\r<BR>\n" );
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document.write( "2x = -1\r<BR>\n" );
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document.write( "x = -1/2\r<BR>\n" );
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document.write( "2x - 1 = 0\r<BR>\n" );
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document.write( "2x = 1\r<BR>\n" );
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document.write( "x = 1/2\r<BR>\n" );
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document.write( "We have 4 values of x:\r<BR>\n" );
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document.write( "x = -2, x = 2, x = -1/2 and x = 1/2\r<BR>\n" );
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document.write( "Are they all values of x?\r<BR>\n" );
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document.write( "The only way to find is to plug all found values of x into the original equation...the equation that was given to you and simplify.\r<BR>\n" );
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document.write( "If you get the same answer on both sides of the equation, then you will know which is the correct value of x or if they all are correct values of x.\r<BR>\n" );
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document.write( "I'll let you do the checking.\r<BR>\n" );
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document.write( "If you do not understand what I did , write back.\r<BR>\n" );
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document.write( "You said:<BR>\n" );
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document.write( "\"Thanks for your promptly reply....Still have a quesion...Why you need to separate the original equation in 2 parts?? Why you need to factorize each one and the final one...How can I identify when is needed to separate & calculate the factor in an equation?\"\r<BR>\n" );
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document.write( "My New Reply:<BR>\n" );
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document.write( "I separated the original equation into two parts to do something that is called factoring by groups.  When you have a polynomial of 4 terms, the easiest way to factor is to set up two groups, factor each group individually, set each factor to zero and solve for x.<BR>\n" );
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document.write( "To check your values of x, plug every value of x that you found into the original polynomial given.<BR>\n" );
document.write( "If you get the same answer on both sides of the equation, you will know that your values of x are right.<BR>\n" );
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document.write( "Do you understand?\r<BR>\n" );
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document.write( "If not, write back.\r<BR>\n" );
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