document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=107867>Question 107867</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is for Introductory Algebra (College).  Instructions are to FACTOR BY GROUPING.  My instructor said to \"arbitrarily change a positive to a negative if necessary to get the correct answer\".  That just doesn't make sense to me.  I have a tendency to over-think things and I really want to know why and how I get to the correct answer.  Is it really possible to just randomly make things up in math????? <BR>\n" );
document.write( "I will show my work.  Thank you in advance for any help you can give as you will likely be keeping me out of a straight-jacket at this point!\r<BR>\n" );
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document.write( "original problem to be factored by grouping: <BR>\n" );
document.write( "p^2-2p-3rp+6r<BR>\n" );
document.write( "my work:  <BR>\n" );
document.write( "(p^2-2p)-1(3rp+6r)<BR>\n" );
document.write( "(p^2-2p)+(-3rp-6r)<BR>\n" );
document.write( "p(p-2) -3r(p+2)  OR  p(p-2) +3r(-p-2)  (THIS IS WHERE IT GOES DOWNHILL!!)<BR>\n" );
document.write( "(?????)(p-3r) ... Final Answer is SUPPOSED to be (p-2)(p-3r)\r<BR>\n" );
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document.write( "Obviously I will never get that as an answer at the rate I am going.\r<BR>\n" );
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document.write( "Again, thank you for any possible help.\r<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 #78628 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=78628\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E2-2p-3rp%2B6r ALIGN=MIDDLE  ALT=\"p%5E2-2p-3rp%2B6r\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E2-2p%2B-3rp%2B6r ALIGN=MIDDLE  ALT=\"p%5E2-2p%2B-3rp%2B6r\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite -3rp as + -3rp. Remember adding a negative is the same as subtracting\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p%5E2-2p%29%2B%28-3rp%2B6r%29 ALIGN=MIDDLE  ALT=\"%28p%5E2-2p%29%2B%28-3rp%2B6r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28p-2%29%2B%28-3rp%2B6r%29 ALIGN=MIDDLE  ALT=\"p%28p-2%29%2B%28-3rp%2B6r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF p out of the first group\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28p-2%29-3r%28p-2%29 ALIGN=MIDDLE  ALT=\"p%28p-2%29-3r%28p-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF -3r out of the second group\r<BR>\n" );
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document.write( "Notice how we have a common factor of p-2, so we can now combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p-3r%29%28p-2%29 ALIGN=MIDDLE  ALT=\"%28p-3r%29%28p-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "Notice how <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p-3r%29%28p-2%29 ALIGN=MIDDLE  ALT=\"%28p-3r%29%28p-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > foils back to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E2-2p-3rp%2B6r ALIGN=MIDDLE  ALT=\"p%5E2-2p-3rp%2B6r\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So this verifies our answer\r<BR>\n" );
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document.write( "note: you made an error on your second step. When you factor out a negative 1 you should get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p%5E2-2p%29-1%283rp-6r%29 ALIGN=MIDDLE  ALT=\"%28p%5E2-2p%29-1%283rp-6r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > not <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p%5E2-2p%29-1%283rp%2B6r%29 ALIGN=MIDDLE  ALT=\"%28p%5E2-2p%29-1%283rp%2B6r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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