document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178745>Question 1178745</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you please help with the following problem in factoring polynomials? \r<BR>\n" );
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document.write( "Factor the common factor out of each expression.\r<BR>\n" );
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document.write( "20 − 35n^2 − 20n^3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #808135 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=808135\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Perhaps this is from the same student as a number of other similar questions I am seeing at this forum today....<br><BR>\n" );
document.write( "In this expression, the coefficients are all multiples of 5, so 5 can be part of the greatest common factor (GCF).  So the expression can be factored as<br><BR>\n" );
document.write( "5(4-7n^2-4n^3)  [1]<br><BR>\n" );
document.write( "Not all the terms contain powers of the variable n, so there is no n in the GCF.<br><BR>\n" );
document.write( "You might want to write the polynomial factor in standard form -- with decreasing powers of the variable:<br><BR>\n" );
document.write( "5(-4n^3-7n^2+4)  [2]<br><BR>\n" );
document.write( "And you might want to include the negative sign as part of the GCF, so that the leading coefficient of the polynomial factor is positive:<br><BR>\n" );
document.write( "-5(4n^2+7n^2-4)  [3]<br><BR>\n" );
document.write( "Those three factorizations are equivalent; it is BAD TEACHING to say that any of them is wrong, or that only one of them is \"correct\".<br><BR>\n" );
document.write( "The act of factoring an expression is never the end goal in solving a problem; it is a step in the process of solving a bigger problem.  In a particular problem, any one of the forms shown might be the best one to use, in terms of making the solution of the overall problem as simple as possible.<br><BR>\n" );
document.write( "It might even be the case that the most useful factorization is<br><BR>\n" );
document.write( "-5(-4+7n^2+4n^3)  [4]<br><BR>\n" );
document.write( "That one is awkward; but it is mathematically correct.<br><BR>\n" );
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